The chip firing game and matroid complexes. (English) Zbl 0998.05010

Merino, Criel

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

Keywords:

chip-firing game; Tutte polynomial; simplicial complex; cographic matroid