The Chip Firing Game and Matroid Complexes

@inproceedings{Merino2001TheCF,
  title={The Chip Firing Game and Matroid Complexes},
  author={Criel Merino},
  booktitle={DM-CCG},
  year={2001}
}
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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Combinatorics and Commutative Algebra

  • R. P. Stanley
  • volume 41 of Progress in mathematics. Birkhuser…
  • 1996
Highly Influential
10 Excerpts

Homology and shellability of matroids and geometric lattices

  • A. Björner
  • N. White, editor, Matroid Applications…
  • 1992
Highly Influential
3 Excerpts

Draft

  • M. K. Chari. Acyclic orientations, the reliability polynomial
  • October
  • 2000
1 Excerpt

Chip-firing and the Tutte polynomial

  • C. Merino
  • Ann. Comb., 1(3):253–259
  • 1997
2 Excerpts

Chip-firing and the chromatic polynomial

  • N. Biggs, P. Winkler
  • Research Report LSE– CDAM–97–03, CDAM
  • 1997

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