[Complexes simpliciaux et systèmes de clôture induits par les relations d'indistinguabilité]
In this paper, we develop in a more general mathematical context the notion of indistinguishability, which in graph theory has recently been investigated as a symmetry relation with respect to a fixed vertex subset. The starting point of our analysis is to consider a set Ω of functions defined on a universe set U and to define an equivalence relation
Nous développons dans ce texte la notion d'indistinguabilité dans un contexte mathématique plus général. Cette notion a en effet été récemment étudiée en théorie des graphes, comme une relation de symétrie relativement aux sommets fixés. Le point de départ de notre analyse est de considérer un ensemble Ω de fonctions définies sur un ensemble univers U et de définir pour tout sous-ensemble
Accepté le :
Publié le :
Giampiero Chiaselotti 1 ; Tommaso Gentile 1 ; Federico Infusino 1
@article{CRMATH_2017__355_9_991_0, author = {Giampiero Chiaselotti and Tommaso Gentile and Federico Infusino}, title = {Simplicial complexes and closure systems induced by indistinguishability relations}, journal = {Comptes Rendus. Math\'ematique}, pages = {991--1021}, publisher = {Elsevier}, volume = {355}, number = {9}, year = {2017}, doi = {10.1016/j.crma.2017.09.010}, language = {en}, }
TY - JOUR AU - Giampiero Chiaselotti AU - Tommaso Gentile AU - Federico Infusino TI - Simplicial complexes and closure systems induced by indistinguishability relations JO - Comptes Rendus. Mathématique PY - 2017 SP - 991 EP - 1021 VL - 355 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2017.09.010 LA - en ID - CRMATH_2017__355_9_991_0 ER -
%0 Journal Article %A Giampiero Chiaselotti %A Tommaso Gentile %A Federico Infusino %T Simplicial complexes and closure systems induced by indistinguishability relations %J Comptes Rendus. Mathématique %D 2017 %P 991-1021 %V 355 %N 9 %I Elsevier %R 10.1016/j.crma.2017.09.010 %G en %F CRMATH_2017__355_9_991_0
Giampiero Chiaselotti; Tommaso Gentile; Federico Infusino. Simplicial complexes and closure systems induced by indistinguishability relations. Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 991-1021. doi : 10.1016/j.crma.2017.09.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.010/
[1] Euler's “De Partitio numerorum”, Bull. Amer. Math. Soc., Volume 44 (2007) no. 4, pp. 561-573
[2] Recognizing Helly edge path tree graphs and their clique graphs, Discrete Appl. Math., Volume 159 (2011), pp. 1166-1175
[3] Improved approximation of maximum vertex coverage problem on bipartite graphs, SIAM J. Discrete Math., Volume 28 (2014) no. 3, pp. 1137-1151
[4] The maximum vertex coverage problem on bipartite graphs, Discrete Appl. Math., Volume 165 (2014), pp. 37-48
[5] On the Galois lattice of bipartite distance hereditary graphs, Discrete Appl. Math., Volume 190 (2015), pp. 13-23
[6] Orthogonal partitions in designed experiments, Des. Codes Cryptogr., Volume 8 (1996) no. 3, pp. 45-77
[7] Association Schemes: Designed Experiments, Algebra and Combinatorics, Cambridge University Press, Cambridge, UK, 2004 (387 p)
[8] Hypergraphs: Combinatorics of Finite Sets, Elsevier, Amsterdam, 1984
[9] Generated envelopes, J. Math. Anal. Appl., Volume 172 (1993), pp. 179-190
[10] An extension principle for closure operators, J. Math. Anal. Appl., Volume 198 (1996), pp. 1-24
[11] Lattice Theory, American Mathematical Society, Providence, Rhode Island, 1967
[12] A class of lattices and boolean functions related to the Manickam–Miklös–Singhi conjecture, Adv. Geom., Volume 13 (2013) no. 1, pp. 1-27
[13] A natural extension of the Young partition lattice, Adv. Geom., Volume 15 (2015) no. 3, pp. 263-280
[14] Micro and macro models of granular computing induced by the indiscernibility relation, Inf. Sci., Volume 388–389 (2017), pp. 247-273
[15] Dominance order on signed partitions, Adv. Geom., Volume 17 (2017) no. 1, pp. 5-29
[16] Orderly algorithm to enumerate central groupoids and their graphs, Acta Math. Sin. Engl. Ser., Volume 23 (2007) no. 2, pp. 249-264
[17] Rectangular groupoids and related structures, Discrete Math., Volume 313 (2013), pp. 1409-1418
[18] On the connection of hypergraph theory with formal concept analysis and rough set theory, Inf. Sci., Volume 330 (2016), pp. 342-357
[19] A new discrete dynamical system of signed integer partitions, Eur. J. Comb., Volume 55 (2016), pp. 119-143
[20] Eulerian stratification of polyhedra, Adv. Appl. Math., Volume 21 (1998), pp. 22-57
[21] The geometric cone relations for simplicial and cubical complexes, Discrete Math., Volume 183 (1998), pp. 39-46
[22] Graph homotopy and Graham homotopy, Discrete Math., Volume 241 (2001), pp. 153-170
[23] Intersection properties of maximal directed cuts in digraphs, Discrete Math., Volume 340 (2017), pp. 3171-3175
[24] New results related to a conjecture of Manickam and Singhi, Eur. J. Comb., Volume 29 (2008) no. 2, pp. 361-368
[25] Parallel and sequential dynamics of two discrete models of signed integer partitions, Appl. Math. Comput., Volume 232 (2014), pp. 1249-1261
[26] Simple graphs in granular computing, Inf. Sci., Volume 340–341 (2016), pp. 279-304
[27] Dependency structures for decision tables, Int. J. Approx. Reason., Volume 88 (2017), pp. 333-370
[28] Knowledge pairing systems in granular computing, Knowl.-Based Syst., Volume 124 (2017), pp. 144-163
[29] The adjacency matrix of a graph as a data table. A geometric perspective, Ann. Mat. Pura Appl., Volume 196 (2017) no. 3, pp. 1073-1112
[30] G. Chiaselotti, T. Gentile, F. Infusino, P. Oliverio, Local dissymmetry on graphs and related algebraic structures, preprint.
[31] Graph Theory, Grad. Texts Math., Springer, 2010
[32] Identifying the minimal transversals of a hypergraph and related problems, SIAM J. Comput., Volume 24 (1995), pp. 1278-1304
[33] On the complexity of monotone dualization and generating minimal hypergraph transversals, Discrete Appl. Math., Volume 32 (2008) no. 2, pp. 171-187
[34] Asymmetric graphs, Acta Math. Hung., Volume 14 (1963) no. 3–4, pp. 295-315
[35] Formal Concept Analysis. Mathematical Foundations, Springer-Verlag, 1999
[36] Power contexts and their concept lattices, Discrete Math., Volume 311 (2011), pp. 2049-2063
[37] Hypergraph families with bounded edge cover or transversal number, Combinatorica, Volume 3 (1983) no. 3–4, pp. 351-358
[38] Lower bounds for three algorithms for transversal hypergraph generation, Discrete Appl. Math., Volume 157 (2009), pp. 1460-1469
[39] Graph Symmetry. Algebraic Methods and Applications (G. Hahn; G. Sabidussi, eds.), NATO ASI Ser., vol. 497, Springer, 1997
[40] Metric and symmetric spaces, Proc. Amer. Math. Soc., Volume 43 (1974) no. 2, pp. 428-430
[41] Nullity-based matroid of rough sets and its application to attribute reduction, Inf. Sci., Volume 263 (2014), pp. 153-165
[42] A bijective toolkit for signed partitions, Ann. Comb., Volume 15 (2011), pp. 95-117
[43] On transitive Cayley graphs of groups and semigroups, Eur. J. Comb., Volume 24 (2003) no. 1, pp. 59-72
[44] Directed graphs and combinatorial properties of semigroups, J. Algebra, Volume 251 (2002) no. 1, pp. 16-26
[45] Cayley graphs as classifiers for data mining: the influence of asymmetries, Discrete Math., Volume 309 (2009), pp. 5360-5369
[46] Metrization of symmetric spaces and regular maps, Proc. Amer. Math. Soc., Volume 35 (1972), pp. 269-274
[47] Orthogonality preserving transformations on indefinite inner product spaces: generalization of Uhlhorn's version of Wigner's theorem, J. Funct. Anal., Volume 194 (2002), pp. 248-262
[48] A Geometry of Approximation. Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns, Springer, 2008
[49] Union-closed families, J. Comb. Theory, Ser. A, Volume 59 (1992), pp. 253-268
[50] Sequential dynamical systems over words, Ann. Comb., Volume 10 (2006) no. 4, pp. 481-498
[51] Combinatorics of sequential dynamical systems, Discrete Math., Volume 308 (2008) no. 4, pp. 514-528
[52] A matroidal approach to rough set theory, Theor. Comput. Sci., Volume 471 (2013), pp. 1-11
[53] Symmetry transformations in indefinite metric spaces: a generalization of Wigner's theorem, Physica A, Volume 127 (1984) no. 3, pp. 599-612
[54] Matroid Theory, Academic Press, 1976
[55] Rough matroids based on relations, Inf. Sci., Volume 232 (2013), pp. 241-252
Cité par Sources :
Commentaires - Politique