Sand piles models of signed partitions with \(d\) piles
type: Item
instance of: scholarly article
title: Sand piles models of signed partitions with \(d\) piles
zbMATH Open document ID: 1264.05007
DOI: 10.1155/2013/615703
author: G. Chiaselotti
author: Cinzia Bisi
author: Paolo A. Oliverio
published in: ISRN Combinatorics
publication date: 2013-06-03T00:00:00Z
review text: Summary: Let \(r, d \leq n\) be nonnegative integers. In this paper we study the basic properties of a discrete dynamical model of signed integer partitions that we denote by \(S(n, d, r)\). A generic element of this model is a signed integer partition with exactly \(d\) all distinct nonzero parts, whose maximum positive summand is not exceeding \(r\) and whose minimum negative summand is not less than \(-(n - r)\). In particular, we determine the covering relations, the rank function, and the parallel convergence time from the bottom to the top of \(S(n, d, r)\) by using an abstract sand piles model with three evolution rules. The lattice \(S(n, d, r)\) was introduced by the first two authors in order to study some combinatorial extremal sum problems.
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 6169808
zbMATH Keywords: discrete dynamical model of signed integer partitions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/615703
OpenAlex ID: W2050374672
Wikidata QID: Q58996720
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description: scientific article; zbMATH DE number 6169808