Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001
Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)
DMTCS Conference Volume AA (2001), pp. 245-256
| author: | Criel Merino |
|---|---|
| title: | The Chip Firing Game and Matroid Complexes |
| keywords: | Chip-firing game, Tutte polynomial, Simplicial complex |
| 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 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. |
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