On the Toppling of a Sand Pile

Jean-Christophe Novelli (1) , Dominique Rossin (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

In this paper, we provide the first study of the sand pile model SPM(0) where we assume that all the grains are numbered with a distinct integer.We obtain a lower bound on the number of terminal sand piles by establishing a bijection between a subset of these sand piles and the set of shifted Young tableaux. We then prove that this number is at least factorial.

Keywords: Sand Pile Model; Young Tableaux

Domains: Computer Science [cs]; Combinatorics [math.CO]; Computational Geometry [cs.CG]; Discrete Mathematics [cs.DM]

Jean-Christophe Novelli, Dominique Rossin. On the Toppling of a Sand Pile. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. pp.275-286, ⟨10.46298/dmtcs.2283⟩. ⟨hal-01182963⟩