Table of Contents
ISRN Combinatorics
Volume 2013, Article ID 615703, 7 pages
http://dx.doi.org/10.1155/2013/615703
Research Article

Sand Piles Models of Signed Partitions with Piles

1Dipartimento di Matematica e Informatica, Universitá di Ferrara, Via Machiavelli 35, 44121 Ferrara, Italy
2Dipartimento di Matematica, Universitá della Calabria, Via Pietro Bucci, Cubo 30B, 87036 Arcavacata di Rende, Italy

Received 3 October 2012; Accepted 4 November 2012

Academic Editors: J. F. Fang, N. A. Gordon, and M.-J. Jou

Copyright © 2013 C. Bisi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be nonnegative integers. In this paper we study the basic properties of a discrete dynamical model of signed integer partitions that we denote by . A generic element of this model is a signed integer partition with exactly all distinct nonzero parts, whose maximum positive summand is not exceeding and whose minimum negative summand is not less than . In particular, we determine the covering relations, the rank function, and the parallel convergence time from the bottom to the top of by using an abstract Sand Piles Model with three evolution rules. The lattice was introduced by the first two authors in order to study some combinatorial extremal sum problems.