Relevant bibliographies by topics / Combinatorics of cores

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Combinatorics of cores'

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Published: 5 October 2024

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Journal articles on the topic "Combinatorics of cores"

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Aukerman, David, Ben Kane, and Lawrence Sze. "On simultaneous s-cores/t-cores." Discrete Mathematics 309, no. 9 (May 2009): 2712–20. http://dx.doi.org/10.1016/j.disc.2008.06.024.

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Godsil, Chris, and Gordon F. Royle. "Cores of Geometric Graphs." Annals of Combinatorics 15, no. 2 (May 15, 2011): 267–76. http://dx.doi.org/10.1007/s00026-011-0094-5.

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Mančinska, Laura, Irene Pivotto, David E. Roberson, and Gordon F. Royle. "Cores of cubelike graphs." European Journal of Combinatorics 87 (June 2020): 103092. http://dx.doi.org/10.1016/j.ejc.2020.103092.

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Han, Guo-Niu, and Ken Ono. "Hook Lengths and 3-Cores." Annals of Combinatorics 15, no. 2 (May 15, 2011): 305–12. http://dx.doi.org/10.1007/s00026-011-0096-3.

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Sato, Cristiane M. "On the robustness of randomk-cores." European Journal of Combinatorics 41 (October 2014): 163–82. http://dx.doi.org/10.1016/j.ejc.2014.03.007.

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Malen, Greg. "Homomorphism complexes andk-cores." Discrete Mathematics 341, no. 9 (September 2018): 2567–74. http://dx.doi.org/10.1016/j.disc.2018.06.014.

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Cho, Hyunsoo, and Kyounghwan Hong. "Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores." Discrete Mathematics 345, no. 9 (September 2022): 112949. http://dx.doi.org/10.1016/j.disc.2022.112949.

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Baruah, Nayandeep Deka, and Kallol Nath. "Infinite families of arithmetic identities for self-conjugate 5-cores and 7-cores." Discrete Mathematics 321 (April 2014): 57–67. http://dx.doi.org/10.1016/j.disc.2013.12.019.

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Thiel, Marko, and Nathan Williams. "Strange expectations and simultaneous cores." Journal of Algebraic Combinatorics 46, no. 1 (April 10, 2017): 219–61. http://dx.doi.org/10.1007/s10801-017-0754-6.

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Kotsireas, Ilias S., Christos Koukouvinos, and Jennifer Seberry. "Hadamard ideals and Hadamard matrices with two circulant cores." European Journal of Combinatorics 27, no. 5 (July 2006): 658–68. http://dx.doi.org/10.1016/j.ejc.2005.03.004.

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Dissertations / Theses on the topic "Combinatorics of cores"

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Stockwell, Roger James. "Frameproof codes : combinatorial properties and constructions." Thesis, Royal Holloway, University of London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405211.

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Houghten, Sheridan. "On combinatorial searches for designs and codes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0016/NQ43587.pdf.

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Phillips, Linzy. "Erasure-correcting codes derived from Sudoku & related combinatorial structures." Thesis, University of South Wales, 2013. https://pure.southwales.ac.uk/en/studentthesis/erasurecorrecting-codes-derived-from-sudoku--related-combinatorial-structures(b359130e-bfc2-4df0-a6f5-55879212010d).html.

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This thesis presents the results of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures. The research identifies that both of the structures contain a number of smaller sub-structures, the removal of which results in a grid with more than one potential solution - a detrimental property for erasure correction purposes. Extensive investigation into the properties of these sub-structures is carried out for each of the two outline erasure correction schemes, and results are determined that indicate that, although the schemes are theoretically feasible, the prevalence of sub-structures results in practically infeasible schemes. The thesis presents detailed classifications for the different cases of sub-structures observed in each of the outline erasure correction schemes. The anticipated similarities in the sub-structures of Sudoku and sub-structures of Latin Squares, an established area of combinatorial research, are observed and investigated, the proportion of Sudoku puzzles free of small sub-structures is calculated and a simulation comparing the recovery rates of small sub-structure free Sudoku and standard Sudoku is carried out. The analysis of sub-structures for the second erasure correction scheme involves detailed classification of a variety of small sub-structures; the thesis also derives probabilistic lower bounds for the expected numbers of case-specific sub-structures within the puzzle structure, indicating that specific types of sub-structure hinder recovery to such an extent that the scheme is infeasible for practical erasure correction. The consequences of complex cell inter-relationships and wider issues with puzzle-based erasure correction, beyond the structures investigated in the thesis are also discussed, concluding that while there are suggestions in the literature that Sudoku and other puzzle-based combinatorial structures may be useful for erasure correction, the work of this thesis suggests that this is not the case.
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Esterle, Alexandre. "Groupes d'Artin et algèbres de Hecke sur un corps fini." Thesis, Amiens, 2018. http://www.theses.fr/2018AMIE0061/document.

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Nous déterminons dans cette thèse l'image des groupes de Artin associés à des groupes de Coxeter irréductibles dans leur algèbre de Iwahori-Hecke finie associée. Cela a été fait en type A dans des articles de Brunat, Marin et Magaard. Dans le cas générique, la clôture de l'image de Zariski a été déterminée dans tous les cas par Marin. L'approximation forte suggère que les résultats devraient être similaire dans le cas fini. Il est néanmoins impossible d'utiliser l'approximation forte sans utiliser de lourdes hypothèses et limiter l'étendue des résultats. Nous démontrons dans cette thèse que les résultats sont similaires mais que de nouveaux phénomènes interviennent de par la complexification des extensions de corps considérées. Les arguments principaux proviennent de la théorie des groupes finis. Nous utiliserons notamment un Théorème de Guralnick et Saxl qui utilise la classification des groupes finis simples pour les représentations de hautes dimensions. Ce théorème donne des conditions pour que des sous-groupes de groupes linéaires soient des groupes classiques dans une représentation naturelle. En petite dimension, nous utiliserons la classification des sous-groupes maximaux des groupes classiques de Bray, Holt et Roney-Dougal pour les cas les plus compliqués
In this doctoral thesis, we will determine the image of Artin groups associated to all finite irreducible Coxeter groups inside their associated finite Iwahori-Hecke algebra. This was done in type A in articles by Brunat, Marin and Magaard. The Zariski closure of the image was determined in the generic case by Marin. It is suggested by strong approximation that the results should be similar in the finite case. However, the conditions required to use are much too strong and would only provide a portion of the results. We show in this thesis that they are but that new phenomena arise from the different field factorizations. The techniques used in the finite case are very different from the ones in the generic case. The main arguments come from finite group theory. In high dimension, we will use a theorem by Guralnick-Saxl which uses the classification of finite simple groups to give a condition for subgroups of linear groups to be classical groups in a natural representation. In low dimension, we will mainly use the classification of maximal subgroups of classical groups obtained by Bray, Holt and Roney-Dougal for the complicated cases
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Paegelow, Raphaël. "Action des sous-groupes finis de SL2(C) sur la variété de carquois de Nakajima du carquois de Jordan et fibrés de Procesi." Electronic Thesis or Diss., Université de Montpellier (2022-....), 2024. http://www.theses.fr/2024UMONS005.

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Dans cette thèse de doctorat, nous avons, dans un premier temps, étudié la décomposition en composantes irréductibles du lieu des points fixes sous l’action d’un sous-groupe fini Γ de SL2(C) de la variété de carquois de Nakajima du carquois de Jordan. La variété de carquois associé au carquois de Jordan est isomorphe soit au schéma ponctuel de Hilbert dans C2 soit à l’espace de Calogero-Moser. Nous avons décrit ces composantes irréductibles à l’aide de variétés de carquois du carquois de McKay associé au sous-groupe fini Γ. Nous nous sommes ensuite intéressés à la combinatoire découlant de l’ensemble d’indexation de ces composantes irréductibles en utilisant une action du groupe de Weyl affine introduite par Nakajima. De plus, nous avons construit un modèle combinatoire lorsque Γ est de type D, qui est le seul cas original et remarquable. En effet, si Γ est de type A, un tel travail a déjà été fait par Iain Gordon et si Γ est de type E, nous avons montré que les points fixes qui sont aussi des points fixes du tore diagonal maximal de SL2(C) sont les idéaux monomiaux du schéma ponctuel de Hilbert dans C2 indexés par les partitions en escaliers. De manière plus précise, si Γ est de type D, nous avons obtenu un modèle de l’ensemble indexant les composantes irréductibles contenant un point fixe du tore maximal diagonal de SL2(C) en termes de partitions symétriques. Enfin, si n est un entier plus grand que 1, en utilisant la classification des résolutions projectives et symplectiques de la singularité (C2)n/Γn où Γn est le produit en couronne du groupe symétrique Sn des n premiers entiers et de Γ, nous avons obtenu une description de toutes ces résolutions projectives et symplectiques en termes de composantes irréductibles du lieu des Γ-points fixes du schéma ponctuel de Hilbert dans C2.Dans un second temps, nous nous sommes intéressés à la restriction de deux fibrés vectoriels au-dessus d’une composante irréductible du lieu des Γ-points fixes du schéma de Hilbert dans C2 fixée. Le premier fibré est le fibré tautologique dont nous avons exprimé la restriction en termes de fibrés tautologiques de Nakajima sur la variété de carquois du carquois de McKay associée à la composante irréductible fixée. Le second fibré vectoriel est le fibré de Procesi. Ce fibré a été introduit par Marc Haiman dans ces travaux démontrant la conjecture n!. Nous avons étudié les fibres de ce fibré en tant que (Sn × Γ)-module. Dans la première partie du chapitre de cette thèse consacré au fibré de Procesi, nous avons démontré un théorème de réduction qui exprime le (Sn × Γ)-module associé à la fibre de la restriction du fibré de Procesi au-desus d’une composante irréductible C du lieu des Γ-points fixes du schéma de Hilbert de n points dans C2 comme l’induit de la fibre de la restriction du fibré de Procesi au-dessus d’une composante irréductible du lieu des Γ-points fixes du schéma de Hilbert de k points dans C2 où l’entier k ≤ n est explicite et dépend de la composante irréductible C et de Γ. Ce théorème est ensuite démontré avec d’autres outils dans deux cas particuliers pour Γ de type A. Enfin, lorsque Γ est de type D, certaines formules explicites de réduction des fibres de la restriction du fibré de Procesi au lieu des Γ-point fixes ont étéobtenues.Pour finir, si l est un entier plus grand que 1, alors dans le cas où Γ est le sous-groupe cyclique d’ordre l contenu dans le tore maximal diagonal de SL2(C) noté µl, le théorème de réduction restreint l’étude des fibres du fibré de Procesi au-dessus du lieu des µl-points fixes du schéma ponctuel de Hilbert dans C2 à l’étude des fibres au-dessus des points du schéma de Hilbert associés aux idéaux monomiaux paramétrés par les l-cœurs. Les (Sn × µl)-modules que l’on obtient semble être reliés à l’espace de Fock de l’algèbre de Kac-Moody ˆsll(C). Une conjecture dans ce sens est énoncée dans le dernier chapitre
In this doctoral thesis, first of all, we have studied the decomposition into irreducible components of the fixed point locus under the action of Γ a finite subgroup of SL2(C) of the Nakajima quiver variety of Jordan’s quiver. The quiver variety associated with Jordan’s quiver is either isomorphic to the punctual Hilbert scheme in C2 or to the Calogero-Moser space. We have described the irreducible components using quiver varieties of McKay’s quiver associated with the finite subgroup Γ. We were then interested in the combinatorics coming out of the indexing set of these irreducible components using an action of the affine Weyl group introduced by Nakajima. Moreover, we have constructed a combinatorial model when Γ is of type D, which is the only original and remarkable case. Indeed, when Γ is of type A, such work has already been done by Iain Gordon and if Γ is of type E, we have shown that the fixed points that are also fixed under the maximal diagonal torus of SL2(C) are the monomial ideals of the punctual Hilbert scheme in C2 indexed by staircase partitions. To be more precise, when Γ is of type D, we have obtained a model of the indexing set of the irreducible components containing a fixed point of the maximal diagonal torus of SL2(C) in terms of symmetric partitions. Finally, if n is an integer greater than 1, using the classification of the projective, symplectic resolutions of the singularity (C2)n/Γn where Γn is the wreath product of the symmetric group on n letters Sn with Γ, we have obtained a description of all such resolutions in terms of irreducible components of the Γ-fixedpoint locus of the Hilbert scheme of points in C2.Secondly, we were interested in the restriction of two vector bundles over a fixed irreducible component of the Γ-fixed point locus of the punctual Hilbert scheme in C2. The first vector bundle is the tautological vector bundle that we have expressed the restriction in terms of Nakajima’s tautological vector bundle on the quiver variety of McKay’s quiver associated with the fixed irreducible component. The second vector bundle is the Procesi bundle. This vector bundle was introduced by Marc Haiman in his work proving the n! conjecture. We have studied the fibers of this bundle as (Sn × Γ)-module. In the first part of the chapter of this thesis dedicated to the Procesi bundle, we have shown a reduction theorem that expresses the (Sn × Γ)-module associated with the fiber of the restriction of the Procesi bundle over an irreducible component C of the Γ-fixed point locus of Hilbert scheme of n points in C2 as the induced of the fiber of the restriction of the Procesi bundle over an irreducible component of the Γ-fixed point locus of the Hilbert scheme of k points in C2 where k ≤ n is explicit and depends on the irreducible component C and Γ. This theorem is then proven with other tools in two edge cases when Γ is of type A. Finally, when Γ is of type D, some explicit reduction formulas of the restriction of the Procesi bundle to the Γ-fixed point locus have been obtained.To finish, if l is an integer greater than 1, then in the case where Γ is the cyclic group of order l contained in the maximal diagonal torus of SL2(C) denoted by µl, the reduction theorem restricts the study of the fibers of the Procesi bundle over the µl-fixed points of the punctual Hilbert scheme in C2 to the study of the fibers over points in the Hilbert scheme associated with monomial ideals parametrized by the l-cores. The (Sn × Γ)-module that one obtains seems to be related to the Fock space of the Kac-Moody algebra ˆsll(C). A conjecture in this direction has been stated in the last chapter
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Paris, Gabrielle. "Resolution of some optimisation problems on graphs and combinatorial games." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1180/document.

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J'ai étudié trois problèmes d'optimisation dans les graphes et les jeux combinatoires.Tout d'abord, les codes identifiants dans les graphes où les sommets font faces à des failles: les codes cherchent à repérer les failles pour les réparer. On s'est intéressé aux codes identifiants dans les graphes circulants en utilisant des plongements de ces graphes dans des grilles infinies.Ensuite, j'ai étudié le jeu de marquage de sommets et le jeu de coloration d'arêtes: ici deux joueurs se font face, le premier cherche à construire une coloration correcte (ou un marquage correct) et le deuxième cherche à l'en empêcher. Pour le jeu de marquage on s'est intéressé aux changements de stratégie gagnante lorsqu'on modifie le graphe. Pour le jeu de coloration d'arêtes on a donné une stratégie gagnante pour le premier joueur pourvu que le graphe considéré admette une certaine décomposition sur les arêtes. On améliore notamment des résultats sur les graphes planaires.Enfin j'ai étudié les jeux à tas purement de casse: deux joueurs à tour de rôle prennent un tas et le cassent en un certain nombre de tas non vides. On s'intéresse aux stratégies gagnantes lorsque les joueurs jouent sur un unique tas contenant n jetons. Ces jeux de pure casse semblent, à l'oeil nu, être réguliers. On a montré que c'est effectivement le cas pour certains et on a donné un test qui permet de déterminer la régularité cas par cas. Un seul cas ne semble pas correspondre à cette régularité: son comportement reste un mystère.En conclusion, je me suis intéressé à trois problèmes bilatéraux qui utilisent différentes méthodes et qui remplissent des propos différents dans le domaine de la combinatoire
I studied three optimization problems on graphs and combinatorial games.First, identifying codes were studied : vertices couteract faults. Identifying codes help locate the fault to repare it. We focused on circulant graphs by embedding them on infinite grids.Then, the marking and the coloring games were studied : two player games were one player wants to build something (a proper coloration or a proper marking) and the other wants to prevent the first player from doing so. For the marking game we studied the evolution of the strategy when modifying the graph. For the coloring game we defined a new edge-wise decomposition of graphs and we defined a new strategy on this decomposition that improves known results on planar graphs.In the end, I studied pure breaking games : two players take turns to break a heap of tokens in a given number of non-empty heaps. We focused on winning strategies for the game starting with a unique heap on n tokens. These games seem, on first sight, to be all regular : we showed this is the case for some of them and we gave a test to study one game at a time. Only one of these games does not seem to be regular, its behavior remains a mystery.To sum up, I studied three bilateral problems that use different methods and have different purposes in combinatorics
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Chen, Lei. "Construction of structured low-density parity-check codes : combinatorial and algebraic approaches /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2005. http://uclibs.org/PID/11984.

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Vandomme, Elise. "Contributions to combinatorics on words in an abelian context and covering problems in graphs." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GRENM010/document.

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Cette dissertation se divise en deux parties, distinctes mais connexes, qui sont le reflet de la cotutelle. Nous étudions et résolvons des problèmes concernant d'une part la combinatoire des mots dans un contexte abélien et d'autre part des problèmes de couverture dans des graphes. Chaque question fait l'objet d'un chapitre. En combinatoire des mots, le premier problème considéré s'intéresse à la régularité des suites au sens défini par Allouche et Shallit. Nous montrons qu'une suite qui satisfait une certaine propriété de symétrie est 2-régulière. Ensuite, nous appliquons ce théorème pour montrer que les fonctions de complexité 2-abélienne du mot de Thue--Morse ainsi que du mot appelé ''period-doubling'' sont 2-régulières. Les calculs et arguments développés dans ces démonstrations s'inscrivent dans un schéma plus général que nous espérons pouvoir utiliser à nouveau pour prouver d'autres résultats de régularité. Le deuxième problème poursuit le développement de la notion de mot de retour abélien introduite par Puzynina et Zamboni. Nous obtenons une caractérisation des mots sturmiens avec un intercepte non nul en termes du cardinal (fini ou non) de l'ensemble des mots de retour abélien par rapport à tous les préfixes. Nous décrivons cet ensemble pour Fibonacci ainsi que pour Thue--Morse (bien que cela ne soit pas un mot sturmien). Nous étudions la relation existante entre la complexité abélienne et le cardinal de cet ensemble. En théorie des graphes, le premier problème considéré traite des codes identifiants dans les graphes. Ces codes ont été introduits par Karpovsky, Chakrabarty et Levitin pour modéliser un problème de détection de défaillance dans des réseaux multiprocesseurs. Le rapport entre la taille optimale d'un code identifiant et la taille optimale du relâchement fractionnaire d'un code identifiant est comprise entre 1 et 2 ln(|V|)+1 où V est l'ensemble des sommets du graphe. Nous nous concentrons sur les graphes sommet-transitifs, car nous pouvons y calculer précisément la solution fractionnaire. Nous exhibons des familles infinies, appelées quadrangles généralisés, de graphes sommet-transitifs pour lesquelles les solutions entière et fractionnaire sont de l'ordre |V|^k avec k dans {1/4, 1/3, 2/5}. Le second problème concerne les (r,a,b)-codes couvrants de la grille infinie déjà étudiés par Axenovich et Puzynina. Nous introduisons la notion de 2-coloriages constants de graphes pondérés et nous les étudions dans le cas de quatre cycles pondérés particuliers. Nous présentons une méthode permettant de lier ces 2-coloriages aux codes couvrants. Enfin, nous déterminons les valeurs exactes des constantes a et b de tout (r,a,b)-code couvrant de la grille infinie avec |a-b|>4. Il s'agit d'une extension d'un théorème d'Axenovich
This dissertation is divided into two (distinct but connected) parts that reflect the joint PhD. We study and we solve several questions regarding on the one hand combinatorics on words in an abelian context and on the other hand covering problems in graphs. Each particular problem is the topic of a chapter. In combinatorics on words, the first problem considered focuses on the 2-regularity of sequences in the sense of Allouche and Shallit. We prove that a sequence satisfying a certain symmetry property is 2-regular. Then we apply this theorem to show that the 2-abelian complexity functions of the Thue--Morse word and the period-doubling word are 2-regular. The computation and arguments leading to these results fit into a quite general scheme that we hope can be used again to prove additional regularity results. The second question concerns the notion of return words up to abelian equivalence, introduced by Puzynina and Zamboni. We obtain a characterization of Sturmian words with non-zero intercept in terms of the finiteness of the set of abelian return words to all prefixes. We describe this set of abelian returns for the Fibonacci word but also for the Thue-Morse word (which is not Sturmian). We investigate the relationship existing between the abelian complexity and the finiteness of this set. In graph theory, the first problem considered deals with identifying codes in graphs. These codes were introduced by Karpovsky, Chakrabarty and Levitin to model fault-diagnosis in multiprocessor systems. The ratio between the optimal size of an identifying code and the optimal size of a fractional relaxation of an identifying code is between 1 and 2 ln(|V|)+1 where V is the vertex set of the graph. We focus on vertex-transitive graphs, since we can compute the exact fractional solution for them. We exhibit infinite families, called generalized quadrangles, of vertex-transitive graphs with integer and fractional identifying codes of order |V|^k with k in {1/4,1/3,2/5}. The second problem concerns (r,a,b)-covering codes of the infinite grid already studied by Axenovich and Puzynina. We introduce the notion of constant 2-labellings of weighted graphs and study them in four particular weighted cycles. We present a method to link these labellings with covering codes. Finally, we determine the precise values of the constants a and b of any (r,a,b)-covering code of the infinite grid with |a-b|>4. This is an extension of a theorem of Axenovich
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Larico, Mullisaca Celso Ever. "Un Algoritmo GRASP-Reactivo para resolver el problema de cortes 1D." Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2010. https://hdl.handle.net/20.500.12672/2649.

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Se tiene un grupo de requerimientos de piezas con una cantidad ilimitada de barras de algún tipo de material de tamaño estándar y éste posee mayor dimensión que el grupo de requerimientos. El problema de cortes 1D describe la utilización de las barras de tamaño estándar realizando cortes sobre ellas, de manera que se satisfaga todos los requerimientos con el menor número de barras de tamaño estándar. El problema es catalogado como NP-Difícil [Garey+79], y es ampliamente aplicado en diversos sectores de la industria tales como la maderera, vidrio, papelera, siderúrgica, etc. La presente tesis propone dos algoritmos GRASP Reactivo para el problema de cortes 1D, basado en los algoritmos GRASP BFD y GRASP FFD propuestos por [Mauricio+02], además, desarrolla un sistema de optimización basado en los algoritmos propuesto. Se realizan experimentos numéricos del algoritmo propuesto sobre 100 instancias de pruebas, de donde se obtiene una eficiencia promedio de 97.04% y una eficiencia ponderada de 97,19% para el GRASP Reactivo BFD con proceso de mejoría, además se observa que el GRASP BFD con proceso de mejoría converge más rápido al encontrar una solución, donde realiza en promedio 1237 iteraciones. Los resultados numéricos muestran una mejora del GRASP Reactivo con respecto al GRASP básico implementado por Ganoza y Solano [Ganoza+02] que obtuvo una eficiencia promedio de 96.73%. Estas mejorías se pueden explicar porque el parámetro de relajación y se ajusta de manera automática y es guiada en la búsqueda de una mejor solución.
It has a set of requirements of parts with an unlimited number of bars of some kind of standard size and material and this has increased the group size requirements. The cutting stock problem 1D describes the use of standard-size bars of making cuts on them, so that it meets all requirements with the least number of standard size bars. The problem is listed as NP-Hard [Garey+79], and is widely used in various industry sectors such as wood, glass, paper, steel, and so on. This thesis proposes two algorithms Reactive GRASP to the cutting stock problem 1D, based on the algorithms GRASP BFD and GRASP FFD proposed by [Mauricio+02], also, developed an optimization system based on the proposed algorithms. Numerical experiments are conducted of the proposed algorithm on 100 instances of testing, where you get an average efficiency of 97.04% and a weighted efficiency of 97,04%, also be seen that the GRASP BFD with improvement converges faster to find a solution average of 1237 iterations. The numerical results show an improvement of reactive GRASP with respect to the basic GRASP implemented by Ganoza and Solano [Ganoza+02], who obtained an average efficiency of 96,73%. These improvements can be explained as the relaxation parameter and is set automatically and is guided in the search for a better solution.
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Passuello, Alberto. "Semidefinite programming in combinatorial optimization with applications to coding theory and geometry." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00948055.

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We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence number of a graph. This hierarchy is based on matrices arising from simplicial complexes. We show some properties that our hierarchy shares with other classical ones. As an example, we show its application to the problem of determining the independence number of Paley graphs.
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Books on the topic "Combinatorics of cores"

1

1951-, Cohen G., ed. Covering codes. Amsterdam: Elsevier, 1997.

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Tonchev, Vladimir. Combinatorial configurations: Designs, codes, graphs. Harlow, Essex, England: Longman Scientific & Technical, 1988.

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Tonchev, Vladimir D. Combinatorial configurations: Designs, codes, graphs. Harlow: Longman Scientific & Technical, 1988.

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Vladimir, Tonchev, ed. Codes, designs, and geometry. Boston: Kluwer Academic Pub., 1996.

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Gerardus Joannes Maria Van Wee. Covering codes, perfect codes, and codes from algebraic curves. Helmond [Netherlands]: Wibro Dissertatiedrukkerij, 1991.

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Beth, Thomas, and Michael Clausen, eds. Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0039172.

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1949-, Beth Thomas, and Clausen Michael, eds. Applicable algebra, error-correcting codes, combinatorics and computer algebra: Proceedings. Berlin: Springer-Verlag, 1988.

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D, Key J., ed. Designs and their codes. Cambridge: Cambridge University Press, 1992.

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Victor, Zinoviev, ed. Codes on Euclidean spheres. Amsterdam: Elsevier, 2001.

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Tonchev, Vladimir. Codes, Designs and Geometry. Boston, MA: Springer US, 1996.

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Book chapters on the topic "Combinatorics of cores"

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Jukna, Stasys. "Combinatorics of Codes." In Texts in Theoretical Computer Science. An EATCS Series, 237–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17364-6_17.

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Shokrollahi, Amin. "LDPC Codes: An Introduction." In Coding, Cryptography and Combinatorics, 85–110. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7865-4_5.

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Ahmed, Maya, Jesús De Loera, and Raymond Hemmecke. "Polyhedral Cones of Magic Cubes and Squares." In Algorithms and Combinatorics, 25–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55566-4_2.

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Rehfinger, Thomas, N. Suresh Babu, and Karl-Heinz Zimmermann. "New Good Codes via CQuest — A System for the Silicon Search of Linear Codes." In Algebraic Combinatorics and Applications, 294–306. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-59448-9_19.

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Li, Lei, and Shoulun Long. "New Constructions of Constant-Weight Codes." In Coding, Cryptography and Combinatorics, 209–22. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7865-4_13.

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Sheekey, John. "13. MRD codes: constructions and connections." In Combinatorics and Finite Fields, edited by Kai-Uwe Schmidt and Arne Winterhof, 255–86. Berlin, Boston: De Gruyter, 2019. http://dx.doi.org/10.1515/9783110642094-013.

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Patrou, Bruno. "Zigzag codes and z-free hulls." In Combinatorics and Computer Science, 263–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61576-8_88.

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Guo, Yuqi, Yun Liu, and Shoufeng Wang. "Some Common-Used Codes." In Topics on Combinatorial Semigroups, 27–75. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-9171-6_2.

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Solé, Patrick. "Covering codes and combinatorial optimization." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 426–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54522-0_130.

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Giulietti, Massimo, Arianna Sabatini, and Marco Timpanella. "PIR Codes from Combinatorial Structures." In Arithmetic of Finite Fields, 169–82. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-22944-2_10.

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Conference papers on the topic "Combinatorics of cores"

1

Sabary, Omer, Inbal Preuss, Ryan Gabrys, Zohar Yakhini, Leon Anavy, and Eitan Yaakobi. "Error-Correcting Codes for Combinatorial Composite DNA." In 2024 IEEE International Symposium on Information Theory (ISIT), 109–14. IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619334.

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Aydin, Nuh, Thomas Guidotti, and Peihan Liu. "New Linear Codes as Quasi-Twisted Codes from Long Constacyclic Codes." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383237.

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Aggarwal, Divesh, Yevgeniy Dodis, and Shachar Lovett. "Non-malleable codes from additive combinatorics." In STOC '14: Symposium on Theory of Computing. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2591796.2591804.

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Rousseva, Assia, and Ivan Landjev. "Codes related to caps and the non-existence of some Griesmer codes." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383359.

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Chee, Yeow Meng, Fei Gao, Samuel Tien Ho Teo, and Hui Zhang. "Combinatorial systematic switch codes." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282453.

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Zhang, Hui, Eitan Yaakobi, and Natalia Silberstein. "Multiset combinatorial batch codes." In 2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017. http://dx.doi.org/10.1109/isit.2017.8006916.

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Verma, Ram Krishna, Om Prakash, and Ashutosh Singh. "Quantum codes from skew constacyclic codes over Fp m + vFp m + v2Fp m." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383402.

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Sidorenko, Vladimir, Wenhui Li, and Gerhard Kramer. "On interleaved rank metric codes." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383406.

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Daskalov, Rumen, and Elena Metodieva. "New QC Codes over GF(11)." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383337.

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Boyvalenkov, P., K. Delchev, D. V. Zinoviev, and V. A. Zinoviev. "On two-weight (linear and nonlinear) codes." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383353.

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Reports on the topic "Combinatorics of cores"

1

Altstein, Miriam, and Ronald J. Nachman. Rational Design of Insect Control Agent Prototypes Based on Pyrokinin/PBAN Neuropeptide Antagonists. United States Department of Agriculture, August 2013. http://dx.doi.org/10.32747/2013.7593398.bard.

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The general objective of this study was to develop rationally designed mimetic antagonists (and agonists) of the PK/PBAN Np class with enhanced bio-stability and bioavailability as prototypes for effective and environmentally friendly pest insect management agents. The PK/PBAN family is a multifunctional group of Nps that mediates key functions in insects (sex pheromone biosynthesis, cuticular melanization, myotropic activity, diapause and pupal development) and is, therefore, of high scientific and applied interest. The objectives of the current study were: (i) to identify an antagonist biophores (ii) to develop an arsenal of amphiphilic topically active PK/PBAN antagonists with an array of different time-release profiles based on the previously developed prototype analog; (iii) to develop rationally designed non-peptide SMLs based on the antagonist biophore determined in (i) and evaluate them in cloned receptor microplate binding assays and by pheromonotropic, melanotropic and pupariation in vivo assays. (iv) to clone PK/PBAN receptors (PK/PBAN-Rs) for further understanding of receptor-ligand interactions; (v) to develop microplate binding assays for screening the above SMLs. In the course of the granting period A series of amphiphilic PK/PBAN analogs based on a linear lead antagonist from the previous BARD grant was synthesized that incorporated a diverse array of hydrophobic groups (HR-Suc-A[dF]PRLa). Others were synthesized via the attachment of polyethylene glycol (PEG) polymers. A hydrophobic, biostablePK/PBAN/DH analog DH-2Abf-K prevented the onset of the protective state of diapause in H. zea pupae [EC50=7 pmol/larva] following injection into the preceding larval stage. It effectively induces the crop pest to commit a form of ‘ecological suicide’. Evaluation of a set of amphiphilic PK analogs with a diverse array of hydrophobic groups of the formula HR-Suc-FTPRLa led to the identification of analog T-63 (HR=Decyl) that increased the extent of diapause termination by a factor of 70% when applied topically to newly emerged pupae. Another biostablePK analog PK-Oic-1 featured anti-feedant and aphicidal properties that matched the potency of some commercial aphicides. Native PK showed no significant activity. The aphicidal effects were blocked by a new PEGylated PK antagonist analog PK-dF-PEG4, suggesting that the activity is mediated by a PK/PBAN receptor and therefore indicative of a novel and selective mode-of-action. Using a novel transPro mimetic motif (dihydroimidazole; ‘Jones’) developed in previous BARD-sponsored work, the first antagonist for the diapause hormone (DH), DH-Jo, was developed and shown to block over 50% of H. zea pupal diapause termination activity of native DH. This novel antagonist development strategy may be applicable to other invertebrate and vertebrate hormones that feature a transPro in the active core. The research identifies a critical component of the antagonist biophore for this PK/PBAN receptor subtype, i.e. a trans-oriented Pro. Additional work led to the molecular cloning and functional characterization of the DH receptor from H. zea, allowing for the discovery of three other DH antagonist analogs: Drosophila ETH, a β-AA analog, and a dF analog. The receptor experiments identified an agonist (DH-2Abf-dA) with a maximal response greater than native DH. ‘Deconvolution’ of a rationally-designed nonpeptide heterocyclic combinatorial library with a cyclic bis-guanidino (BG) scaffold led to discovery of several members that elicited activity in a pupariation acceleration assay, and one that also showed activity in an H. zea diapause termination assay, eliciting a maximal response of 90%. Molecular cloning and functional characterization of a CAP2b antidiuretic receptor from the kissing bug (R. prolixus) as well as the first CAP2b and PK receptors from a tick was also achieved. Notably, the PK/PBAN-like receptor from the cattle fever tick is unique among known PK/PBAN and CAP2b receptors in that it can interact with both ligand types, providing further evidence for an evolutionary relationship between these two NP families. In the course of the granting period we also managed to clone the PK/PBAN-R of H. peltigera, to express it and the S. littoralis-R Sf-9 cells and to evaluate their interaction with a variety of PK/PBAN ligands. In addition, three functional microplate assays in a HTS format have been developed: a cell-membrane competitive ligand binding assay; a Ca flux assay and a whole cell cAMP ELISA. The Ca flux assay has been used for receptor characterization due to its extremely high sensitivity. Computer homology studies were carried out to predict both receptor’s SAR and based on this analysis 8 mutants have been generated. The bioavailability of small linear antagonistic peptides has been evaluated and was found to be highly effective as sex pheromone biosynthesis inhibitors. The activity of 11 new amphiphilic analogs has also been evaluated. Unfortunately, due to a problem with the Heliothis moth colony we were unable to select those with pheromonotropic antagonistic activity and further check their bioavailability. Six peptides exhibited some melanotropic antagonistic activity but due to the low inhibitory effect the peptides were not further tested for bioavailability in S. littoralis larvae. Despite the fact that no new antagonistic peptides were discovered in the course of this granting period the results contribute to a better understanding of the interaction of the PK/PBAN family of Nps with their receptors, provided several HT assays for screening of libraries of various origin for presence of PK/PBAN-Ragonists and antagonists and provided important practical information for the further design of new, peptide-based insecticide prototypes aimed at the disruption of key neuroendocrine physiological functions in pest insects.
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