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  1. Home > Articles & Issues >
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  3. The Chip Firing Game ...
Conference paper

The Chip Firing Game and Matroid Complexes

Criel Merino (1) (2)
(1) Instituto de Matematicas
(2) Centro de Ciencias Matemáticas [México]
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Imported on
November 21, 2016
Published on
December 31, 2000
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
Proceedings
DOI
10.46298/dmtcs.2278
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https://about.hal.science/hal-authorisation-v1
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The Chip Firing Game and Matroid Complexes

Criel Merino (1) (2)
(1) Instituto de Matematicas
(2) Centro de Ciencias Matemáticas [México]
Abstract
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.
Keywords
  • [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]
  • Chip-firing game
  • Tutte polynomial
  • Simplicial complex
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