On the Toppling of a Sand Pile

Abstract

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
• [info] computer science [cs]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-cg] computer science [cs]/computational geometry [cs.cg]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]