Two Self-Dual Lattices of Signed Integer Partitions

Authors

Giampiero Chiaselotti, Dipartimento di Matematica e Informatica, Universit´a della Calabria, Via Pietro Bucci, Cubo 30B, 87036 Arcavacata di Rende (CS), ItalyFollow
William Keith
Paolo A. Oliverio

Author Country (or Countries)

Italy

Abstract

In this paper we study two self-dual lattices of signed integer partitions, D(m,n) and E(m,n), which can be considered also sub-lattices of the lattice L(m,2n), where L(m,n) is the lattice of all the usual integer partitions with at most m parts and maximum part not exceeding n. We also introduce the concepts of k-covering poset for the signed partitions and we show that D(m,n) is 1-covering and E(m,n) is 2-covering.We study D(m,n) and E(m,n) as two discrete dynamical models with some evolution rules. In particular, the 1-covering lattices are exactly the lattices definable with one outside addition rule and one outside deletion rule. The 2-covering lattices have further need of another inside-switch rule.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/080661

Recommended Citation

Chiaselotti, Giampiero; Keith, William; and A. Oliverio, Paolo (2014) "Two Self-Dual Lattices of Signed Integer Partitions," Applied Mathematics & Information Sciences: Vol. 08: Iss. 6, Article 61.
DOI: http://dx.doi.org/10.12785/amis/080661
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss6/61