Criel Merino - The Chip Firing Game and Matroid Complexes

dmtcs:2278 - Discrete Mathematics & Theoretical Computer Science, January 1, 2001, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) - https://doi.org/10.46298/dmtcs.2278
The Chip Firing Game and Matroid ComplexesArticle

Authors: Criel Merino 1

  • 1 Instituto de Matematicas

In this paper we construct from a cographic matroid M, a pure multicomplex whose degree sequence is the h―vector of the the matroid complex of M. This result provesa conjecture of Richard Stanley [Sta96] in the particular case of cographic matroids. We also prove that the multicomplexes constructed are M―shellable, so proving a conjecture of Manoj Chari [Cha97] again in the case of cographic matroids. The proofs use results on a game for graphs called the chip firing game.

https://doi.org/10.46298/dmtcs.2278
Source: HAL:hal-01182958v1
Volume: DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
Section: Proceedings
Published on: January 1, 2001
Imported on: November 21, 2016
Keywords: Chip-firing game,Tutte polynomial,Simplicial complex,[INFO] Computer Science [cs],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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