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The chip firing game and matroid complexes. (English) Zbl 0998.05010
Discrete models: combinatorics, computation, and geometry. Proceedings of the 1st international conference (DM-CCG), Paris, France, July 2-5, 2001. Paris: Maison de l’Informatique et des Mathématiques Discrètes (MIMD), Discrete Math. Theor. Comput. Sci., Proc. AA, 245-256, electronic only (2001).
Summary: We construct from a cographic matroid $$M$$, a pure multicomplex whose degree sequence is the $$h$$-vector of the matroid complex of $$M$$. This result proves a conjecture of Richard Stanley (1996) in the particular case of cographic matroids. We also prove that the multicomplexes constructed are $$M$$-shellable, so proving a conjecture of Manoj Chari (1997) again in the case of cographic matroids. The proofs use results on a game for graphs called the chip firing game.
For the entire collection see [Zbl 0985.00015].

##### MSC:
 05B35 Combinatorial aspects of matroids and geometric lattices
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