The Chip Firing Game and Matroid Complexes

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 provesa 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.

Locations

• Discrete Mathematics & Theoretical Computer Science - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF