The Chip Firing Game and Matroid Complexes

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.
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Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.245-256, 2001, DMTCS Proceedings
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Criel Merino. The Chip Firing Game and Matroid Complexes. Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.245-256, 2001, DMTCS Proceedings. 〈hal-01182958〉

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