The Chip Firing Game and Matroid Complexes

  title={The Chip Firing Game and Matroid Complexes},
  author={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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