|title:||The Chip Firing Game and Matroid Complexes|
|keywords:||Chip-firing game, Tutte polynomial, Simplicial complex|
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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|reference:||Criel Merino (2001), The Chip Firing Game and Matroid Complexes, in Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 245-256|
|bibtex:||For a corresponding BibTeX entry, please consider our BibTeX-file.|
|ps.gz-source:||dmAA0118.ps.gz (37 K)|
|ps-source:||dmAA0118.ps (101 K)|
|pdf-source:||dmAA0118.pdf (113 K)|
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