DMTCS Proceedings, Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

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The Chip Firing Game and Matroid Complexes

Criel Merino


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 proves a 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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