Relevant bibliographies by topics / Simplicial complexes and polytopes

Academic literature on the topic 'Simplicial complexes and polytopes'

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Published: 25 May 2024

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Journal articles on the topic "Simplicial complexes and polytopes"

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Bruns, W., and J. Gubeladze. "Combinatorial Invariance of Stanley–Reisner Rings." gmj 3, no. 4 (August 1996): 315–18. http://dx.doi.org/10.1515/gmj.1996.315.

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Abstract In this short note we show that Stanley–Reisner rings of simplicial complexes, which have had a “dramatic application” in combinatorics [Hibi, Algebraic Combinatorics on Convex Polytopes, Carslaw Publications, 1992, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.
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Erokhovets, N. Yu. "Buchstaber invariant theory of simplicial complexes and convex polytopes." Proceedings of the Steklov Institute of Mathematics 286, no. 1 (October 2014): 128–87. http://dx.doi.org/10.1134/s008154381406008x.

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Pournin, Lionel. "Lifting simplicial complexes to the boundary of convex polytopes." Discrete Mathematics 312, no. 19 (October 2012): 2849–62. http://dx.doi.org/10.1016/j.disc.2012.06.005.

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Joswig, Michael. "Projectivities in simplicial complexes and colorings of simple polytopes." Mathematische Zeitschrift 240, no. 2 (June 1, 2002): 243–59. http://dx.doi.org/10.1007/s002090100381.

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Deza, Michel, and Mathieu Dutour Sikirić. "Generalized cut and metric polytopes of graphs and simplicial complexes." Optimization Letters 14, no. 2 (November 13, 2018): 273–89. http://dx.doi.org/10.1007/s11590-018-1358-3.

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Ayzenberg, A. A. "Substitutions of polytopes and of simplicial complexes, and multigraded betti numbers." Transactions of the Moscow Mathematical Society 74 (April 9, 2014): 175–202. http://dx.doi.org/10.1090/s0077-1554-2014-00224-7.

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Santos, Francisco. "Recent progress on the combinatorial diameter of polytopes and simplicial complexes." TOP 21, no. 3 (October 2013): 426–60. http://dx.doi.org/10.1007/s11750-013-0295-7.

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Bahri, Anthony, Soumen Sarkar, and Jongbaek Song. "Infinite families of equivariantly formal toric orbifolds." Forum Mathematicum 31, no. 2 (March 1, 2019): 283–301. http://dx.doi.org/10.1515/forum-2018-0019.

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AbstractThe simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and more generally, polyhedral products. In this paper we extend the analysis to include toric orbifolds. Our main results yield infinite families of toric orbifolds, derived from a given one, whose integral cohomology is free of torsion and is concentrated in even degrees, a property which might be termed integrally equivariantly formal. In all cases, it is possible to give a description of the cohomology ring and to relate it to the cohomology of the original orbifold.
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Beben, Piotr, and Jelena Grbić. "LS-category of moment-angle manifolds and higher order Massey products." Forum Mathematicum 33, no. 5 (August 26, 2021): 1179–205. http://dx.doi.org/10.1515/forum-2021-0015.

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Abstract Using the combinatorics of the underlying simplicial complex K, we give various upper and lower bounds for the Lusternik–Schnirelmann (LS) category of moment-angle complexes 𝒵 K {\mathcal{Z}_{K}} . We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS-category. In particular, we characterize the LS-category of moment-angle complexes 𝒵 K {\mathcal{Z}_{K}} over triangulated d-manifolds K for d ≤ 2 {d\leq 2} , as well as higher-dimensional spheres built up via connected sum, join, and vertex doubling operations. We show that the LS-category closely relates to vanishing of Massey products in H * ⁢ ( 𝒵 K ) {H^{*}(\mathcal{Z}_{K})} , and through this connection we describe first structural properties of Massey products in moment-angle manifolds. Some of the further applications include calculations of the LS-category and the description of conditions for vanishing of Massey products for moment-angle manifolds over fullerenes, Pogorelov polytopes and k-neighborly complexes, which double as important examples of hyperbolic manifolds.
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De Loera, Jesús A. "Comments on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes." TOP 21, no. 3 (October 2013): 474–81. http://dx.doi.org/10.1007/s11750-013-0291-y.

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Dissertations / Theses on the topic "Simplicial complexes and polytopes"

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Cartier, Noémie. "Lattice properties of acyclic pipe dreams." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG065.

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Cette thèse s'inscrit dans le domaine de la combinatoire algébrique. Certains algorithmes de tri peuvent être décrits par des diagrammes appelés réseaux de tri, et l'exécution de ces algorithmes sur des permutations se traduit alors par des arrangements de courbes sur ces réseaux. Ces arrangements donnent des modèles pour des structures combinatoires classiques : par exemple, le treillis de Tamari, dont les relations de couverture sont les rotations sur les arbres binaires, et qui est un quotient bien connu de l'ordre faible sur les permutations. Les complexes de sous-mots généralisent les réseaux de tris et les arrangements de courbes aux groupes de Coxeter. Ils ont des liens profonds en algèbre et géométrie, notamment dans le calcul de Schubert, l'étude des variétés grassmanniennes et la théorie des algèbres amassées. Cette thèse s'intéresse aux structures de treillis sur certains complexes de sous-mots, généralisant les treillis de Tamari. Plus précisément, elle étudie la relation définie par les extensions linéaires des facettes d'un complexe de sous-mot. Dans un premier lieu, nous nous intéressons aux complexes de sous-mots définis sur un mot triangulaire du groupe symétrique, que nous représentons par des arrangements de tuyaux triangulaires. Nous prouvons alors que cette relation définit un quotient de treillis d'un intervalle de l'ordre faible ; par ailleurs, nous pouvons également utiliser cette relation pour définir un morphisme de treillis de cet intervalle au graphe des flips du complexe de sous-mots restreint à certaines de ses facettes. Dans un second lieu, nous étendons notre étude aux complexes de sous-mots définis sur les mots alternants du groupe symétrique. Nous montrons que cette même relation définit également un quotient de treillis ; en revanche, le morphisme associé n'a plus pour image le graphe des flips, mais le squelette du polyhèdre de brique, un objet défini sur les complexes de sous-mots pour étudier des réalisations du multi-associahèdre. Enfin, nous discutons des possibles extensions de ces résultats aux groupes de Coxeter finis, ainsi que de leurs applications pour généraliser certains objets définis en type A comme les treillis de nu-Tamari
This thesis comes within the scope of algebraic combinatorics. Some sorting algorithms can be described by diagrams called sorting networks, and the execution of the algorithms on input permutations translates to arrangements of curves on the networks. These arrangements modelize some classical combinatorial structures: for example, the Tamari lattice, whose cover relations are the rotations on binary trees, and which is a well-known quotient of the weak order on permutations. Subword complexes generalize sorting network and arrangements of curves to Coxeter groups. They have deep connections in algebra and geometry, in particular in Schubert calculus, in the study of grassmannian varieties, and in the theory of cluster algebras. This thesis focuses on lattice structures on some subword complexes, generalizing Tamari lattices. More precisely, it studies the relation defined by linear extensions of the facets of a subword complex. At first we focus on subword complexes defined on a triangular word of the symmetric group, which we represent with triangular pipe dreams. We prove that this relation defines a lattice quotient of a weak order interval; moreover, we can also use this relation to define a lattice morphism from this interval to the restriction of the flip graph of the subword complex to some of its facets. Secondly, we extent our study to subword complexes defined on alternating words of the symmetric group. We prove that this same relation also defines a lattice quotient; however, the image of the associated morphism is no longer the flip graph, but the skeleton of the brick polyhedron, an object defines on subword complexes to study realizations of the multiassociahedron. Finally, we discuss possible extensions of these results to finite Coxeter groups, as well as their applications to generalize some objects defined in type A such as nu-Tamari lattices
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Jonsson, Jakob. "Simplicial Complexes of Graphs." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-202.

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Jonsson, Jakob. "Simplicial complexes of graphs /." Berlin [u.a.] : Springer, 2008. http://dx.doi.org/10.1007/978-3-540-75858-7.

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Mirmohades, Djalal. "Simplicial Structure on Complexes." Licentiate thesis, Uppsala universitet, Algebra och geometri, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-221410.

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Zhang, Zhihan. "Random walk on simplicial complexes." Electronic Thesis or Diss., université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM010.

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La notion de laplacien d’un graphe peut être généralisée aux complexes simpliciaux et aux hypergraphes. Cette notion contient des informations sur la topologie de ces structures. Dans la première partie de cette thèse,nous définissons une nouvelle chaîne de Markov sur les complexes simpliciaux. Pour un degré donné k de simplexes, l’espace d’états n’est pas les k-simplexes comme dans les articles précédents sur ce sujet mais plutôt l’ensemble des k-chaines ou k-co-chaines. Ce nouveau cadre est la généralisation naturelle sur les chaînes de Markov canoniques sur des graphes. Nous montrons que le générateur de notre chaîne de Markov est lié au Laplacien supérieur défini dans le contexte de la topologie algébrique pour structure discrète. Nous établissons plusieurs propriétés clés de ce nouveau procédé. Nous montrons que lorsque les complexes simpliciaux examinés sont une séquence de triangulation du tore plat, les chaînes de Markov tendent vers une forme différentielle valorisée processus continu.Dans la deuxième partie de cette thèse, nous explorons quelques applications de la marche aléatoire, i.e. la détection de trous basée sur la marche aléatoire et les noyaux complexes simpliciaux. Pour la détection de trous basée sur la marche aléatoire, nous introduisons un algorithme pour faire des simulations effectuées pour la marche aléatoire à valeur cyclique (k = 1) sur un complexe simplicial avec trous. Pour les noyaux de complexes simpliciaux, nous étendons la définition des noyaux de graphes basés sur la marche aléatoire afin de mesurer la similitude entre deux complexes simpliciaux
The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs. This notion contains information on the topology of these structures. In the first part of this thesis, we define a new Markov chain on simplicial complexes. For a given degree k of simplices, the state space is not thek-simplices as in previous papers about this subject but rather the set of k-chains or k-cochains.This new framework is the natural generalization on the canonical Markov chains on graphs.We show that the generator of our Markov chainis related to the upper Laplacian defined in the context of algebraic topology for discrete structure. We establish several key properties of this new process. We show that when the simplicial complexes under scrutiny are a sequence of ever refining triangulation of the flat torus, the Markov chains tend to a differential form valued continuous process.In the second part of this thesis, we explore some applications of the random walk, i.e., random walk based hole detection and simplicial complexes kernels. For the random walk based hole detection, we introduce an algorithm tomake simulations carried for the cycle-valuedrandom walk (k = 1) on a simplicial complex with holes. For the simplicial complexes kernels,we extend the definition of random walk based graph kernels in order to measure the similarity between two simplicial complexes
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Zuffi, Lorenzo. "Simplicial Complexes From Graphs Toward Graph Persistence." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13519/.

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Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph theory, we define the persistent block number and the persistent edge-block number.
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Petersson, Anna. "Enumeration of spanning trees in simplicial complexes." Licentiate thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-138976.

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Egan, Sarah. "Nash equilibria in games and simplicial complexes." Thesis, University of Bath, 2008. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500758.

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Nash's Theorem is a famous and widely used result in non-cooperative game theory which can be applied to games where each player's mixed strategy payoff function is defined as an expectation. Current proofs of this Theorem neither justify why this constraint is necessary or satisfactorily identifies its origins. In this Thesis we change this and prove Nash's Theorem for abstract games where, in particular, the payoff functions can be replaced by total orders. The result of this is a combinatoric proof of Nash's Theorem. We also construct a generalised simplicial complex model and demonstrate a more general form of Nash's Theorem holds in this setting. This leads to the realisation Nash's Theorem is not a consequence of a fixed-point theorem but rather a combinatoric phenomenon existing in a much more general mathematical model.
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Hetyei, Gábor. "Simplicial and cubical complexes : anologies and differences." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/32610.

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Perkins, Simon. "Field D* pathfinding in weighted simplicial complexes." Doctoral thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/6433.

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The development of algorithms to efficiently determine an optimal path through a complex environment is a continuing area of research within Computer Science. When such environments can be represented as a graph, established graph search algorithms, such as Dijkstra’s shortest path and A*, can be used. However, many environments are constructed from a set of regions that do not conform to a discrete graph. The Weighted Region Problem was proposed to address the problem of finding the shortest path through a set of such regions, weighted with values representing the cost of traversing the region. Robust solutions to this problem are computationally expensive since finding shortest paths across a region requires expensive minimisation. Sampling approaches construct graphs by introducing extra points on region edges and connecting them with edges criss-crossing the region. Dijkstra or A* are then applied to compute shortest paths. The connectivity of these graphs is high and such techniques are thus not particularly well suited to environments where the weights and representation frequently change. The Field D* algorithm, by contrast, computes the shortest path across a grid of weighted square cells and has replanning capabilites that cater for environmental changes. However, representing an environment as a weighted grid (an image) is not space-efficient since high resolution is required to produce accurate paths through areas containing features sensitive to noise. In this work, we extend Field D* to weighted simplicial complexes – specifically – triangulations in 2D and tetrahedral meshes in 3D.
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Books on the topic "Simplicial complexes and polytopes"

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Jonsson, Jakob. Simplicial Complexes of Graphs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75859-4.

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Simplicial complexes of graphs. Berlin: Springer, 2008.

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Rhodes, John, and Pedro V. Silva. Boolean Representations of Simplicial Complexes and Matroids. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15114-4.

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Hibi, Takayuki. Algebraic combinatorics on convex polytopes. Glebe, NSW, Australia: Carslaw Publications, 1992.

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Mudamburi, Nolan Jatiel Zifambi. Simplicial complexes based on automorphisms of free products. Birmingham: University of Birmingham, 1996.

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Chazelle, B. The complexity of cutting complexes. Urbana, Il (1304 W. Springfield Ave., Urbana 61801): Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1987.

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Ghani, Razia Parvin. Presentation of the automorphism group of free groups using simplicial complexes. Birmingham: University of Birmingham, 1992.

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Ashley, N. Simplicial T-complexes and crossed complexes: A non-abelian version of a theorem of Dold and Kan. Warszawa: Państwowe Wydawn. Nauk., 1988.

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1975-, Panov Taras E., ed. Toric topology. Providence, Rhode Island: American Mathematical Society, 2015.

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Persistence theory: From quiver representations to data analysis. Providence, Rhode Island: American Mathematical Society, 2015.

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Book chapters on the topic "Simplicial complexes and polytopes"

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Hibi, Takayuki. "Ehrhart polynomials of convex polytopes, ℎ-vectors of simplicial complexes, and nonsingular projective toric varieties." In Discrete and Computational Geometry: Papers from the DIMACS Special Year, 165–78. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/006/09.

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Rhodes, John, and Pedro V. Silva. "Simplicial Complexes." In Springer Monographs in Mathematics, 31–37. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15114-4_4.

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Rotman, Joseph J. "Simplicial Complexes." In Graduate Texts in Mathematics, 131–79. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-4576-6_8.

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Deo, Satya. "Simplicial Complexes." In Texts and Readings in Mathematics, 83–122. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8734-9_3.

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Petersen, T. Kyle. "Simplicial complexes." In Eulerian Numbers, 163–83. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-3091-3_8.

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Schmidt, Gunther, and Michael Winter. "Simplicial Complexes." In Relational Topology, 155–81. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74451-3_10.

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McCleary, John. "Simplicial complexes." In The Student Mathematical Library, 151–70. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/stml/031/10.

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Rhodes, John, and Pedro V. Silva. "Paving Simplicial Complexes." In Springer Monographs in Mathematics, 85–103. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15114-4_6.

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Deo, Satya. "Finite Simplicial Complexes." In Texts and Readings in Mathematics, 85–115. Gurgaon: Hindustan Book Agency, 2003. http://dx.doi.org/10.1007/978-93-86279-13-2_3.

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Costa, Armindo, and Michael Farber. "Random Simplicial Complexes." In Springer INdAM Series, 129–53. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31580-5_6.

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Conference papers on the topic "Simplicial complexes and polytopes"

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Popović, Jovan, and Hugues Hoppe. "Progressive simplicial complexes." In the 24th annual conference. New York, New York, USA: ACM Press, 1997. http://dx.doi.org/10.1145/258734.258852.

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Bertolotto, Michela, Leila De Floriani, and Paola Marzano. "Pyramidal simplicial complexes." In the third ACM symposium. New York, New York, USA: ACM Press, 1995. http://dx.doi.org/10.1145/218013.218054.

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Reddy, Thummaluru Siddartha, Sundeep Prabhakar Chepuri, and Pierre Borgnat. "Clustering with Simplicial Complexes." In 2023 31st European Signal Processing Conference (EUSIPCO). IEEE, 2023. http://dx.doi.org/10.23919/eusipco58844.2023.10289740.

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Vergne, A., L. Decreusefond, and P. Martins. "Reduction algorithm for simplicial complexes." In IEEE INFOCOM 2013 - IEEE Conference on Computer Communications. IEEE, 2013. http://dx.doi.org/10.1109/infcom.2013.6566818.

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Isufi, Elvin, and Maosheng Yang. "Convolutional Filtering in Simplicial Complexes." In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2022. http://dx.doi.org/10.1109/icassp43922.2022.9746349.

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Lickorish, W. B. R. "Simplicial moves on complexes and manifolds." In Low Dimensional Topology -- The Kirbyfest. Mathematical Sciences Publishers, 1999. http://dx.doi.org/10.2140/gtm.1999.2.299.

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Preti, Giulia, Gianmarco De Francisci Morales, and Francesco Bonchi. "STruD: Truss Decomposition of Simplicial Complexes." In WWW '21: The Web Conference 2021. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3442381.3450073.

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Sardellitti, Stefania, and Sergio Barbarossa. "Robust Signal Processing Over Simplicial Complexes." In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2022. http://dx.doi.org/10.1109/icassp43922.2022.9746761.

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Sardellitti, Stefania, and Sergio Barbarossa. "Probabilistic Topological Models over Simplicial Complexes." In 2023 57th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2023. http://dx.doi.org/10.1109/ieeeconf59524.2023.10477035.

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Zheng, Hailun. "Face enumeration on flag complexes and flag spheres." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0028.

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