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