an:01741027
Zbl 0998.05010
Merino, Criel
The chip firing game and matroid complexes
EN
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 Math??matiques Discr??tes (MIMD), Discrete Math. Theor. Comput. Sci., Proc. AA, 245-256, electronic only (2001).
2001
a
05B35
chip-firing game; Tutte polynomial; simplicial complex; cographic matroid
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].