Thematische Bibliographien / Combinatorial representation theory

Inhaltsverzeichnis

  1. Zeitschriftenartikel
  2. Dissertationen
  3. Bücher
  4. Buchteile
  5. Konferenzberichte

Auswahl der wissenschaftlichen Literatur zum Thema „Combinatorial representation theory“

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Veröffentlicht am 25. Mai 2024

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Zeitschriftenartikel zum Thema "Combinatorial representation theory"

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Ibarra, Andoni, and Thomas Mormann. "Una teoría combinatoria de las representaciones científicas." Crítica (México D. F. En línea) 32, no. 95 (2000): 3–46. http://dx.doi.org/10.22201/iifs.18704905e.2000.874.

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The aim of this paper is to introduce a new concept of scientific representation into philosophy of science. The new concept -to be called homological or functorial representation- is a genuine generalization of the received notion of representation as a structure preserving map as it is used, for example, in the representational theory of measurement. It may be traced back, at least implicitly, to the works of Hertz and Duhem. A modern elaboration may be found in the foundational discipline of mathematical category theory. In contrast to the familiar concepts of representations, functorial representations do not depend on any notion of similarity, neither structural nor objectual one. Rather, functorial representation establish correlations between the structures of the representing and the represented domains. Thus, they may be said to form a class of quite "non-isomorphic" representations. Nevertheless, and this is the central claim of this paper, they are the most common type of representations used in science. In our paper we give some examples from mathematics and empirical science. One of the most interesting features of the new concept is that it leads in a natural way to a combinatorial theory of scientific representations, i.e. homological or functorial representations do not live in insulation, rather, they may be combined and connected in various ways thereby forming a net of interrelated representations. One of the most important tasks of a theory of scientific representations is to describe this realm of combinatorial possibilities in detail. Some first tentative steps towards this endeavour are done in our paper.
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Malinin, Dmitry. "One combinatorial construction in representation theory." European Journal of Combinatorics 80 (August 2019): 287–95. http://dx.doi.org/10.1016/j.ejc.2018.02.007.

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3

HSIEH, CHUN-CHUNG. "FIRST NON-VANISHING SELF-LINKING OF KNOTS (I) COMBINATORIC AND DIAGRAMMATIC STUDY." Journal of Knot Theory and Its Ramifications 20, no. 12 (2011): 1637–48. http://dx.doi.org/10.1142/s0218216511009510.

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In this paper, following the scheme of [Borromean rings and linkings, J. Geom. Phys.60 (2010) 823–831; Combinatoric and diagrammatic study in knot theory, J. Knot Theory Ramifications16 (2007) 1235–1253; Massey–Milnor linking = Chern–Simons–Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903], we study the first non-vanishing self-linkings of knots, aiming at the study of combinatorial formulae and diagrammatic representation. The upshot of perturbative quantum field theory is to compute the Feynman diagrams explicitly, though it is impossible in general. Along this line in this paper we could not only compute some Feynman diagrams, but also give the explicit and combinatorial formulae.
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Bremner, Murray R., Mikelis G. Bickis, and Mohsen Soltanifar. "Cayley’s hyperdeterminant: A combinatorial approach via representation theory." Linear Algebra and its Applications 437, no. 1 (2012): 94–112. http://dx.doi.org/10.1016/j.laa.2012.01.037.

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SHAI, OFFER. "The multidisciplinary combinatorial approach (MCA) and its applications in engineering." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 15, no. 2 (2001): 109–44. http://dx.doi.org/10.1017/s0890060401152030.

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The current paper describes the Multidisciplinary Combinatorial Approach (MCA), the idea of which is to develop discrete mathematical representations, called “Combinatorial Representations” (CR) and to represent with them various engineering systems. During the research, the properties and methods embedded in each representation and the connections between them were investigated thoroughly, after which they were associated with various engineering systems to solve related engineering problems. The CR developed up until now are based on graph theory, matroid theory, and discrete linear programming, whereas the current paper employs only the first two. The approach opens up new ways of working with representations, reasoning and design, some of which are reported in the paper, as follows: 1) Integrated multidisciplinary representation—systems which contain interrelating elements from different disciplines are represented by the same CR. Consequently, a uniform analysis process is performed on the representation, and thus on the whole system, irrespective of the specific disciplines, to which the elements belong. 2) Deriving known methods and theorems—new proofs to known methods and theorems are derived in a new way, this time on the basis of the combinatorial theorems embedded in the CR. This enables development of a meta-representation for engineering as a whole, through which the engineering reasoning becomes convenient. In the current paper, this issue is illustrated on structural analysis. 3) Deriving novel connections between remote fields—new connections are derived on the basis of the relations between the different combinatorial representations. An innovative connection between mechanisms and trusses, shown in the paper, has been derived on the basis of the mutual dualism between their corresponding CR. This new connection alone has opened several new avenues of research, since knowledge and algorithms from machine theory are now available for use in structural analysis and vice versa. Furthermore, it has opened opportunities for developing new design methods, in which, for instance, structures with special properties are developed on the basis of known mechanisms with special properties, as demonstrated in this paper. Conversely, one can use these techniques to develop special mechanisms from known trusses.
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Armenta, Marco, and Pierre-Marc Jodoin. "The Representation Theory of Neural Networks." Mathematics 9, no. 24 (2021): 3216. http://dx.doi.org/10.3390/math9243216.

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In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical object that we represent using a network quiver. Furthermore, we show that network quivers gently adapt to common neural network concepts such as fully connected layers, convolution operations, residual connections, batch normalization, pooling operations and even randomly wired neural networks. We show that this mathematical representation is by no means an approximation of what neural networks are as it exactly matches reality. This interpretation is algebraic and can be studied with algebraic methods. We also provide a quiver representation model to understand how a neural network creates representations from the data. We show that a neural network saves the data as quiver representations, and maps it to a geometrical space called the moduli space, which is given in terms of the underlying oriented graph of the network, i.e., its quiver. This results as a consequence of our defined objects and of understanding how the neural network computes a prediction in a combinatorial and algebraic way. Overall, representing neural networks through the quiver representation theory leads to 9 consequences and 4 inquiries for future research that we believe are of great interest to better understand what neural networks are and how they work.
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Griffeth, Stephen. "Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r, p, n)." Proceedings of the Edinburgh Mathematical Society 53, no. 2 (2010): 419–45. http://dx.doi.org/10.1017/s0013091508000904.

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AbstractThis paper aims to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category $\mathcal{O}$ for the rational Cherednik algebra of type G(r, p, n). As a first application, a self-contained and elementary proof of the analogue for the groups G(r, p, n), with r > 1, of Gordon's Theorem (previously Haiman's Conjecture) on the diagonal co-invariant ring is given. No restriction is imposed on p; the result for p ≠ r has been proved by Vale using a technique analogous to Gordon's. Because of the combinatorial application to Haiman's Conjecture, the paper is logically self-contained except for standard facts about complex reflection groups. The main results should be accessible to mathematicians working in algebraic combinatorics who are unfamiliar with the impressive range of ideas used in Gordon's proof of his theorem.
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Capparelli, Stefano, Arne Meurman, Andrej Primc, and Mirko Primc. "New partition identities from \(C^{(1)}_\ell\)-modules." Glasnik Matematicki 57, no. 2 (2022): 161–84. http://dx.doi.org/10.3336/gm.57.2.01.

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In this paper we conjecture combinatorial Rogers-Ramanu­jan type colored partition identities related to standard representations of the affine Lie algebra of type \(C^{(1)}_\ell\), \(\ell\geq2\), and we conjecture similar colored partition identities with no obvious connection to representation theory of affine Lie algebras.
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Vershik, A. M., and N. V. Tsilevich. "On the relationship between combinatorial functions and representation theory." Functional Analysis and Its Applications 51, no. 1 (2017): 22–31. http://dx.doi.org/10.1007/s10688-017-0165-4.

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Proctor, Robert A. "A Schensted Algorithm Which Models Tensor Representations of the Orthogonal Group." Canadian Journal of Mathematics 42, no. 1 (1990): 28–49. http://dx.doi.org/10.4153/cjm-1990-002-1.

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This paper is concerned with a combinatorial construction which mysteriously “mimics” or “models” the decomposition of certain reducible representations of orthogonal groups. Although no knowledge of representation theory is needed to understand the body of this paper, a little familiarity is necessary to understand the representation theoretic motivation given in the introduction. Details of the proofs will most easily be understood by people who have had some exposure to Schensted's algorithm or jeu de tacquin.
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Dissertationen zum Thema "Combinatorial representation theory"

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Kreighbaum, Kevin M. "Combinatorial Problems Related to the Representation Theory of the Symmetric Group." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1270830566.

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Liu, Xudong. "MODELING, LEARNING AND REASONING ABOUT PREFERENCE TREES OVER COMBINATORIAL DOMAINS." UKnowledge, 2016. http://uknowledge.uky.edu/cs_etds/43.

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In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representations that extend and combine existing formalisms such as conditional preference nets, lexicographic preference trees, answer-set optimization programs, possibilistic logic, and conditional preference networks; on learning problems that aim at discovering qualitative preference models and predictive preference information from practical data; and on preference reasoning problems centered around qualitative preference optimization and aggregation methods. Applications of my research include recommender systems, decision support tools, multi-agent systems, and Internet trading and marketing platforms.
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Faitg, Matthieu. "Mapping class groups, skein algebras and combinatorial quantization." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS023/document.

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Les algèbres L(g,n,H) ont été introduites par Alekseev-Grosse-Schomerus et Buffenoir-Roche au milieu des années 1990, dans le cadre de la quantification combinatoire de l'espace de modules des G-connexions plates sur la surface S(g,n) de genre g avec n disques ouverts enlevés. L'algèbre de Hopf H, appelée algèbre de jauge, était à l'origine le groupe quantique U_q(g), avec g=Lie(G). Dans cette thèse nous appliquons les algèbres L(g,n,H) à la topologie en basses dimensions (groupe de difféotopie et algèbres d'écheveaux des surfaces), sous l'hypothèse que H est une algèbre de Hopf de dimension finie, factorisable et enrubannée mais pas nécessairement semi-simple, l'exemple phare d'une telle algèbre de Hopf étant le groupe quantique restreint associé à sl(2) (à une racine 2p-ième de l'unité). D'abord, nous construisons en utilisant L(g,n,H) une représentation projective des groupes de difféotopie de S(g,0)D et de S(g,0) (où D est un disque ouvert). Nous donnons des formules pour les représentations d'un ensemble de twists de Dehn qui engendre le groupe de difféotopie; en particulier ces formules nous permettent de montrer que notre représentation est équivalente à celle construite par Lyubashenko-Majid et Lyubashenko via des méthodes catégoriques. Pour le tore S(1,0) avec le groupe quantique restreint associé à sl(2) comme algèbre de jauge, nous calculons explicitement la représentation de SL(2,Z) en utilisant une base convenable de l'espace de représentation et nous en déterminons la structure.Ensuite, nous introduisons une description diagrammatique de L(g,n,H) qui nous permet de définir de façon très naturelle l'application boucle de Wilson W. Cette application associe un élément de L(g,n,H) à chaque entrelac dans (S(g,n)D) x [0,1] qui est parallélisé, orienté et colorié par des H-modules. Quand l'algèbre de jauge est le groupe quantique restreint associé à sl(2), nous utilisons W et les représentations de L(g,n,H) pour construire des représentations des algèbres d'écheveaux S_q(S(g,n)). Pour le tore S(1,0) nous étudions explicitement cette représentation<br>The algebras L(g,n,H) have been introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche in the middle of the 1990's, in the program of combinatorial quantization of the moduli space of flat G-connections over the surface S(g,n) of genus g with n open disks removed. The Hopf algebra H, called gauge algebra, was originally the quantum group U_q(g), with g = Lie(G). In this thesis we apply these algebras L(g,n,H) to low-dimensional topology (mapping class groups and skein algebras of surfaces), under the assumption that H is a finite dimensional factorizable ribbon Hopf algebra which is not necessarily semisimple, the guiding example of such a Hopf algebra being the restricted quantum group associated to sl(2) (at a 2p-th root of unity).First, we construct from L(g,n,H) a projective representation of the mapping class groups of S(g,0)D and of S(g,0) (D being an open disk). We provide formulas for the representations of Dehn twists generating the mapping class group; in particular these formulas allow us to show that our representation is equivalent to the one constructed by Lyubashenko-Majid and Lyubashenko via categorical methods. For the torus S(1,0) with the restricted quantum group associated to sl(2) for the gauge algebra, we compute explicitly the representation of SL(2,Z) using a suitable basis of the representation space and we determine the structure of this representation.Second, we introduce a diagrammatic description of L(g,n,H) which enables us to define in a very natural way the Wilson loop map W. This maps associates an element of L(g,n,H) to any link in (S(g,n)D) x [0,1] which is framed, oriented and colored by H-modules. When the gauge algebra is the restricted quantum group associated to sl(2), we use W and the representations of L(g,n,H) to construct representations of the skein algebras S_q(S(g,n)). For the torus S(1,0) we explicitly study this representation
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Newhouse, Jack. "Explorations of the Aldous Order on Representations of the Symmetric Group." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/35.

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The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. However, by restricting the problem down to Young-Jucys-Murphy elements, the problem becomes explicitly combinatorial. This approach has led to many novel insights, whose proofs are simple and elegant. However, there remain many open questions related to the Aldous Order, both in general and for the Young-Jucys-Murphy elements.
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Assunção, Guilherme Puglia. "Representações retangulares de grafos planares." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-07052012-164622/.

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Uma representação retangular de um grafo plano G é uma representação de G, onde cada vértice é desenhado como um retângulo de modo que dois retângulos devem compartilhar algum segmento de seus lados se e somente se existe uma aresta em G entre os vértices correspondentes aos retângulos. Ainda, a representação de G deve formar um retângulo e não deve existir buracos, ou seja, toda região interna deve corresponder a algum vértice de G. Um desenho retangular de um grafo plano H é um desenho de H, onde todas as arestas são desenhadas como segmentos horizontais ou verticais. Ainda, todas as faces internas são retângulos e as arestas que incidem na face externa também formam um retângulo. Nesta dissertação, apresentamos os principais trabalhos existentes na literatura para problemas associados à representação retangular. Também apresentamos resultados para problemas associados ao desenho retangular. Por fim, apresentamos o algoritmo que desenvolvemos para determinar as coordenadas dos vértices de um desenho retangular quando a orientação das arestas já foram determinadas.<br>A rectangular representation of a plane graph G is a representation of G, where each vertex is drawn as a rectangle, such as two rectangles have to share some boundary if and only if exist an edge in G between the corresponding vertices. Also, the representation of G must form a rectangle and does not contain any holes, in other words, every point inside the formed rectangle must correspond to some vertex of G. A rectangular drawing of a plane graph H is a drawing of H, where all edges are drawn either in vertical or in horizontal. Also, every internal face is a rectangle and the edges which are incident in the external face define a rectangle. In this dissertation, we present the main studies in the literature for problems associated with the rectangular representation. We also present results for problems associated with rectangular drawing. Finally, we present the algorithm we developed to determine the coordinates of the vertices of a rectangular drawing when the orientation of the edges have been determined.
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Teff, Nicholas James. "The Hessenberg Representation." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4919.

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The Hessenberg representation is a representation of the symmetric group afforded on the cohomology ring of a regular semisimple Hessenberg variety. We study this representation via a combinatorial presentation called GKM Theory. This presentation allows for the study of the representation entirely from a graph. The thesis derives a combinatorial construction of a basis of the equivariant cohomology as a free module over a polynomial ring. This generalizes classical constructions of Schubert classes and divided difference operators for the equivariant cohomology of the flag variety.
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Wolfgang, Harry Lewis. "Two interactions between combinatorics and representation theory : monomial immanants and Hochschild cohomology." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43461.

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Meinel, Joanna [Verfasser]. "Affine nilTemperley-Lieb algebras and generalized Weyl algebras: Combinatorics and representation theory / Joanna Meinel." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1122193874/34.

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Tarrago, Pierre. "Non-commutative generalization of some probabilistic results from representation theory." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1123/document.

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Le sujet de cette thèse est la généralisation non-commutative de résultats probabilistes venant de la théorie des représentations. Les résultats obtenus se divisent en trois parties distinctes. Dans la première partie de la thèse, le concept de groupe quantique easy est étendu au cas unitaire. Tout d'abord, nous donnons une classification de l'ensemble des groupes quantiques easy unitaires dans le cas libre et classique. Nous étendons ensuite les résultats probabilistes de au cas unitaire. La deuxième partie de la thèse est consacrée à une étude du produit en couronne libre. Dans un premier temps, nous décrivons les entrelaceurs des représentations dans le cas particulier d'un produit en couronne libre avec le groupe symétrique libre: cette description permet également d'obtenir plusieurs résultats probabilistes. Dans un deuxième temps, nous établissons un lien entre le produit en couronne libre et les algèbres planaires: ce lien mène à une preuve d'une conjecture de Banica et Bichon. Dans la troisième partie de la thèse, nous étudions un analoque du graphe de Young qui encode la structure multiplicative des fonctions fondamentales quasi-symétriques. La frontière minimale de ce graphe a déjà été décrite par Gnedin et Olshanski. Nous prouvons que la frontière minimale coïncide avec la frontière de Martin. Au cours de cette preuve, nous montrons plusieurs résultats combinatoires asymptotiques concernant les diagrammes de Young en ruban<br>The subject of this thesis is the non-commutative generalization of some probabilistic results that occur in representation theory. The results of the thesis are divided into three different parts. In the first part of the thesis, we classify all unitary easy quantum groups whose intertwiner spaces are described by non-crossing partitions, and develop the Weingarten calculus on these quantum groups. As an application of the previous work, we recover the results of Diaconis and Shahshahani on the unitary group and extend those results to the free unitary group. In the second part of the thesis, we study the free wreath product. First, we study the free wreath product with the free symmetric group by giving a description of the intertwiner spaces: several probabilistic results are deduced from this description. Then, we relate the intertwiner spaces of a free wreath product with the free product of planar algebras, an object which has been defined by Bisch and Jones. This relation allows us to prove the conjecture of Banica and Bichon. In the last part of the thesis, we prove that the minimal and the Martin boundaries of a graph introduced by Gnedin and Olshanski are the same. In order to prove this, we give some precise estimates on the uniform standard filling of a large ribbon Young diagram. This yields several asymptotic results on the filling of large ribbon Young diagrams
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Charles, Balthazar. "Combinatorics and computations : Cartan matrices of monoids & minimal elements of Shi arrangements." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG063.

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Cette thèse présente le résultat de recherches sur deux thèmes combinatoires distincts: le calcul effectif des matrices de Cartan en théorie des représentations des monoïdes et l'exploration des propriétés des éléments minimaux dans les arrangements de Shi des groupes de Coxeter. Bien que disparates, ces deux domaines de recherche partagent l'utilisation de méthodes combinatoires et d'exploration informatique, soit en tant que fin en soi pour le premier domaine, soit comme aide à la recherche pour le second. Dans la première partie de la thèse, nous développons des méthodes pour le calcul effectif des tables de caractères et des matrices de Cartan dans la théorie des représentations des monoïdes. À cette fin, nous présentons un algorithme basé sur nos résultats pour le calcul efficace des points fixes sous une action similaire à une conjugaison, dans le but de mettre en œuvre la formule de [Thiéry '12] pour la matrice de Cartan. Après une introduction largement auto-contenue aux notions nécessaires, nous présentons nos résultats sur le comptage des points fixes, ainsi qu'une nouvelle formule pour la table de caractères des monoïdes finis. Nous évaluons les performances des algorithmes résultants en termes de temps d'exécution et d'utilisation mémoire. Nous observons qu'ils sont plus efficaces par plusieurs ordres de grandeur que les algorithmes non spécialisés pour les monoïdes. Nous espérons que l'implémentation (publique) résultant de ces travaux contribuera à la communauté des représentations des monoïdes en permettant des calculs auparavant difficiles. La deuxième partie de la thèse se concentre sur les propriétés des éléments minimaux dans les arrangements de Shi. Les arrangements de Shi ont été introduits dans [Shi '87] et sont l'objet de la Conjecture 2 dans [Dyer, Hohlweg '14]. Initialement motivés par cette conjecture, après une introduction aux notions nécessaires, nous présentons deux résultats. Premièrement, une démonstration directe dans le cas des groupes de rang 3. Deuxièmement, dans le cas particulier des groupes de Weyl, nous donnons une description des éléments minimaux des régions de Shi en étendant une bijection issue de [Athanasiadis, Linusson '99] et [Armstrong, Reiner, Rhoades '15] entre les fonctions de parking et les régions de Shi permettant d'effectuer le calcul pratique des éléments minimaux. Comme application, à partir des propriétés de ce calcul, nous donnons une démonstration de la conjecture pour les groupes de Weyl indépendante de leur classification. Ces résultats révèlent une interaction intrigante entre les partitions non-croisées et non-embrassées dans le cas des groupes de Weyl classiques<br>This thesis presents an investigation into two distinct combinatorial subjects: the effective computation of Cartan matrices in monoid representation theory and the exploration of properties of minimal elements in Shi arrangements of Coxeter groups. Although disparate, both of these research focuses share a commonality in the utilization of combinatorial methods and computer exploration either as an end in itself for the former or as a help to research for the latter. In the first part of the dissertation, we develop methods for the effective computation of character tables and Cartan matrices in monoid representation theory. To this end, we present an algorithm based on our results for the efficient computations of fixed points under a conjugacy-like action, with the goal to implement Thiéry's formula for the Cartan matrix from [Thiéry '12]. After a largely self-contained introduction to the necessary background, we present our results for fixed-point counting, as well as a new formula for the character table of finite monoids. We evaluate the performance of the resulting algorithms in terms of execution time and memory usage and find that they are more efficient than algorithms not specialized for monoids by orders of magnitude. We hope that the resulting (public) implementation will contribute to the monoid representation community by allowing previously impractical computations. The second part of the thesis focuses on the properties of minimal elements in Shi arrangements. The Shi arrangements were introduced in [Shi '87] and are the object of Conjecture 2 from [Dyer, Hohlweg '14]. Originally motivated by this conjecture, we present two results. Firstly, a direct proof in the case of rank 3 groups. Secondly, in the special case of Weyl groups, we give a description of the minimal elements of the Shi regions by extending a bijection from [Athanasiadis, Linusson '99] and [Armstrong, Reiner, Rhoades '15] between parking functions and Shi regions. This allows for the effective computation of the minimal elements. From the properties of this computation, we provide a type-free proof of the conjecture in Weyl groups as an application. These results reveal an intriguing interplay between the non-nesting and non-crossing worlds in the case of classical Weyl groups
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Bücher zum Thema "Combinatorial representation theory"

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Kang, Seok-Jin, and Kyu-Hwan Lee, eds. Combinatorial and Geometric Representation Theory. American Mathematical Society, 2003. http://dx.doi.org/10.1090/conm/325.

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Kazuhiko, Koike, and Nihon Sūgakkai, eds. Combinatorial methods in representation theory. Published for the Mathematical Society of Japan by Kinokuniya, 2000.

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Japan) Conference "Expansion of Combinatorial Representation Theory" (2007 Kyoto. New trends in combinatorial representation theory. Research Institute for Mathematical Sciences, Kyoto University, 2009.

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Conference "Combinatorial Representation Theory and Related Topics" (2006 Kyoto, Japan). Combinatorial representation theory and related topics. Research Institute for Mathematical Sciences, Kyoto University, 2008.

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Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. Kenkyū Shūkai. Topics in combinatorial representation theory: October 11-14, 2011. Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2012.

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A, Kaimanovich Vadim, and Lodkin A. 1945-, eds. Representation theory, dynamical systems, and asymptotic combinatorics. American Mathematical Society, 2006.

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Seok-Jin, Kang, and Lee Kyu-Hwan 1970-, eds. Combinatorial and geometric representation theory: An international conference on combinatorial and geometric representation theory, October 22-26, 2001, Seoul National University, Seoul, Korea. American Mathematical Society, 2003.

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Chari, Vyjayanthi, Jacob Greenstein, Kailash Misra, K. Raghavan, and Sankaran Viswanath, eds. Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory. American Mathematical Society, 2013. http://dx.doi.org/10.1090/conm/602.

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India) International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory (2010 Bangalore. Recent developments in algebraic and combinatorial aspects of representation theory: International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, August 12-16, 2010, National Institute of Advanced Studies, Bangalore, India : Conference on Algebraic and Combinatorial Approaches to Representation Theory, May 18-20, 2012, University of California, Riverside, CA. Edited by Chari, Vyjayanthi, editor of compilation and Conference on Algebraic and Combinatorial Approaches to Representation Theory (2012 : Riverside, Calif.). American Mathematical Society, 2013.

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1959-, Ariki Susumu, ed. Algebraic groups and quantum groups: International Conference on Representation Theory of Algebraic Groups and Quantum Groups, August 2-6, 2010, Nagoya University, Nagoya, Japan. American Mathematical Society, 2012.

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Buchteile zum Thema "Combinatorial representation theory"

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Barot, Michael. "Combinatorial Invariants." In Introduction to the Representation Theory of Algebras. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11475-0_8.

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Kang, Seok-Jin. "Combinatorial Representation Theory and Crystal Bases." In Proceedings of the Third International Algebra Conference. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0337-6_4.

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Brenner, Sheila. "A combinatorial characterisation of finite Auslander-Reiten quivers." In Representation Theory I Finite Dimensional Algebras. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075256.

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Baumslag, Gilbert. "Affine algebraic sets and the representation theory of finitely generated groups." In Topics in Combinatorial Group Theory. Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8587-4_5.

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Lenart, Cristian. "Combinatorial representation theory of Lie algebras. Richard Stanley’s work and the way it was continued." In The Mathematical Legacy of Richard P. Stanley. American Mathematical Society, 2016. http://dx.doi.org/10.1090//mbk/100/15.

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Chen, Yu-Fang, Philipp Rümmer, and Wei-Lun Tsai. "A Theory of Cartesian Arrays (with Applications in Quantum Circuit Verification)." In Automated Deduction – CADE 29. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38499-8_10.

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AbstractWe present a theory of Cartesian arrays, which are multi-dimensional arrays with support for the projection of arrays to sub-arrays, as well as for updating sub-arrays. The resulting logic is an extension of Combinatorial Array Logic (CAL) and is motivated by the analysis of quantum circuits: using projection, we can succinctly encode the semantics of quantum gates as quantifier-free formulas and verify the end-to-end correctness of quantum circuits. Since the logic is expressive enough to represent quantum circuits succinctly, it necessarily has a high complexity; as we show, it suffices to encode the k-color problem of a graph under a succinct circuit representation, an NEXPTIME-complete problem. We present an NEXPTIME decision procedure for the logic and report on preliminary experiments with the analysis of quantum circuits using this decision procedure.
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Rota, Gian-Carlo. "Combinatorics, Representation Theory and Invariant Theory." In Indiscrete Thoughts. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-0-8176-4781-0_3.

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Palmér, Hanna, and Jorryt van Bommel. "Young Students’ Choice of Representation When Solving a Problem-Solving Task on Combinatorics." In Teaching Mathematics as to be Meaningful – Foregrounding Play and Children’s Perspectives. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-37663-4_9.

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AbstractThis paper is about the representations young students use when they are working on a problem-solving task on combinatorics. Results from previous studies on young students and combinatorics have shown connections between the representations used and the extent to which students solved the task. Based on these previous results, young students in this study were interviewed about their choice of representation. In this paper, the rationales expressed by the students are connected to the representation and stage of systematization shown in their documentation. The results indicate that difficulties in representing the context of the problem-solving task may force some of the students to work with a representation on a level of abstraction not suitable for them. Working with representations at an unsuitable level of abstraction may in turn influence how the students manage to complete the problem-solving task.
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Méliot, Pierre-Loïc. "Combinatorics of partitions and tableaux." In Representation Theory of Symmetric Groups. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315371016-4.

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Schnabel, R. "Representation of Graphs by Integers." In Topics in Combinatorics and Graph Theory. Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_73.

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Konferenzberichte zum Thema "Combinatorial representation theory"

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Wu, Kaisheng, Liangda Fang, Liping Xiong, et al. "Automatic Synthesis of Generalized Winning Strategies of Impartial Combinatorial Games Using SMT Solvers." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/236.

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Strategy representation and reasoning has recently received much attention in artificial intelligence. Impartial combinatorial games (ICGs) are a type of elementary and fundamental games in game theory. One of the challenging problems of ICGs is to construct winning strategies, particularly, generalized winning strategies for possibly infinitely many instances of ICGs. In this paper, we investigate synthesizing generalized winning strategies for ICGs. To this end, we first propose a logical framework to formalize ICGs based on the linear integer arithmetic fragment of numeric part of PDDL. We then propose an approach to generating the winning formula that exactly captures the states in which the player can force to win. Furthermore, we compute winning strategies for ICGs based on the winning formula. Experimental results on several games demonstrate the effectiveness of our approach.
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HLINĚNÝ, PETR. "COMBINATORIAL GENERATION OF MATROID REPRESENTATIONS: THEORY AND PRACTICE." In Proceedings of the 3rd Asian Applied Computing Conference. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2007. http://dx.doi.org/10.1142/9781860948534_0001.

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Rumynin, Dmitriy. "Kac-Moody Groups and Their Representations." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0020.

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Sullivan, Eric, Scott Ferguson, and Joseph Donndelinger. "Exploring Differences in Preference Heterogeneity Representation and Their Influence in Product Family Design." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48596.

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When using conjoint studies for market-based design, two model types can be fit to represent the heterogeneity present in a target market, discrete or continuous. In this paper, data from a choice-based conjoint study with 2275 respondents is analyzed for a 19-attribute combinatorial design problem with over 1 billion possible product configurations. Customer preferences are inferred from the choice task data using both representations of heterogeneity. The hierarchical Bayes mixed logit model exemplifies the continuous representation of heterogeneity, while the latent class multinomial logit model corresponds to the discrete representation. Product line solutions are generated by each of these model forms and are then explored to determine why differences are observed in both product solutions and market share estimates. These results reveal some potential limitations of the Latent Class model in the masking of preference heterogeneity. Finally, the ramifications of these results on the market-based design process are discussed.
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Ahmed, Faez, Yaxin Cui, Yan Fu, and Wei Chen. "A Graph Neural Network Approach for Product Relationship Prediction." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-69462.

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Abstract Graph representation learning has revolutionized many artificial intelligence and machine learning tasks in recent years, ranging from combinatorial optimization, drug discovery, recommendation systems, image classification, social network analysis to natural language understanding. This paper shows their efficacy in modeling relationships between products and making predictions for unseen product networks. By representing products as nodes and their relationships as edges of a graph, we show how an inductive graph neural network approach, named GraphSAGE, can efficiently learn continuous representations for nodes and edges. These representations also capture product feature information such as price, brand, and engineering attributes. They are combined with a classification model for predicting the existence of a relationship between any two products. Using a case study of the Chinese car market, we find that our method yields double the F-1 score compared to an Exponential Random Graph Model-based method for predicting the co-consideration relationship between cars. While a vanilla Graph-SAGE requires a partial network to make predictions, we augment it with an ‘adjacency prediction model’ to circumvent this limitation. This enables us to predict product relationships when no neighborhood information is known. Finally, we demonstrate how a permutation-based interpretability analysis can provide insights on how design attributes impact the predictions of relationships between products. Overall, this work provides a systematic method to predict the relationships between products in a complex engineering system.
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Klisura, Ðorže. "Embedding Non-planar Graphs: Storage and Representation." In 7th Student Computer Science Research Conference. University of Maribor Press, 2021. http://dx.doi.org/10.18690/978-961-286-516-0.13.

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In this paper, we propose a convention for repre-senting non-planar graphs and their least-crossing embeddings in a canonical way. We achieve this by using state-of-the-art tools such as canonical labelling of graphs, Nauty’s Graph6 string and combinatorial representations for planar graphs. To the best of our knowledge, this has not been done before. Besides, we implement the men-tioned procedure in a SageMath language and compute embeddings for certain classes of cubic, vertex-transitive and general graphs. Our main contribution is an extension of one of the graph data sets hosted on MathDataHub, and towards extending the SageMath codebase.
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Xu, Jieping, and William T. Rhodes. "State-space representation for multifrequency acoustooptic interactions." In OSA Annual Meeting. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.mp1.

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The theory of acoustooptic (AO) interactions can be established from a wave (diffraction) viewpoint or a particle (photon-photon scattering) viewpoint. Recently the theory of Feynman diagrams was used with some success to further develop a scattering-based theory of acoustooptic interactions. We have augmented that approach with a state-space representation of the possible scattering interactions. This state-space representation greatly simplifies the combinatoric problems that must be solved to determine scattering amplitudes (diffraction efficiencies) in various acoustooptic diffraction regimes. We have used it to extend the Feynman diagram theory of AO interactions to include the case where an arbitrary number of acoustic frequencies are present in the AO device. No other method, wave- or particle-based, has been successful in this regard. The basic approach is outlined and results are presented for multiple-frequency diffraction in four different regimes: Raman-Nath, isotropic or nondegenerate birefringent Bragg, axial birefringent Bragg, and rediffractable birefringent Bragg.
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Menguy, Grégoire, Sébastien Bardin, Nadjib Lazaar, and Arnaud Gotlieb. "Active Disjunctive Constraint Acquisition." In 20th International Conference on Principles of Knowledge Representation and Reasoning {KR-2023}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/kr.2023/50.

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Constraint acquisition (CA) is a method for learning users' concepts by representing them as a conjunction of constraints. While this approach works well for many combinatorial problems over finite domains, some applications require the acquisition of disjunctive constraints, possibly coming from logical implications or negations. In this paper, we propose the first CA algorithm tailored to the automatic inference of disjunctive constraints, named DCA. A key ingredient there, is to build upon the computation of maximal satisfiable subsets. We demonstrate experimentally that DCA is faster and more effective than traditional CA with added disjunctive constraints, even for ultra-metric constraints with up to 5 variables. We also apply DCA to precondition acquisition in software verification, where it outperforms the previous CA-based approach PreCA, being 2.5 times faster. Specifically, in our evaluation DCA infers more preconditions in just 5 minutes than PreCA does in an hour, without requiring prior knowledge about disjunction size. Our results demonstrate the potential of DCA for improving the efficiency and scalability of constraint acquisition in the disjunctive case, enabling a wide range of novel applications.
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Luo, Kailun, and Yongmei Liu. "Automatic Verification of FSA Strategies via Counterexample-Guided Local Search for Invariants." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/251.

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Strategy representation and reasoning has received much attention over the past years. In this paper, we consider the representation of general strategies that solve a class of (possibly infinitely many) games with similar structures, and their automatic verification, which is an undecidable problem. We propose to represent a general strategy by an FSA (Finite State Automaton) with edges labelled by restricted Golog programs. We formalize the semantics of FSA strategies in the situation calculus. Then we propose an incomplete method for verifying whether an FSA strategy is a winning strategy by counterexample-guided local search for appropriate invariants. We implemented our method and did experiments on combinatorial game and also single-agent domains. Experimental results showed that our system can successfully verify most of them within a reasonable amount of time.
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Cohen, Jaime, Luiz A. Rodrigues, and Elias P. Duarte Jr. "Improved Parallel Implementations of Gusfield’s Cut Tree Algorithm." In Simpósio em Sistemas Computacionais de Alto Desempenho. Sociedade Brasileira de Computação, 2011. http://dx.doi.org/10.5753/wscad.2011.17275.

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This work presents parallel versions of Gusfield’s cut tree algorithm and the proposal of two heuristics aimed at improving their performance. Cut trees are a compact representation of the edge-connectivity between every pair of vertices of an undirected graph. Cut trees have a vast number of applications in combinatorial optimization and in the analysis of networks originated in many applied fields. However, surprisingly few works have been published on the practical performance of cut tree algorithms. This paper describes two parallel versions of Gusfield’s cut tree algorithm and presents extensive experimental results which show a significant speedup on most real and synthetic graphs in our dataset.
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