Two self-dual lattices of signed integer partitions

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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. © 2014 NSP Natural Sciences Publishing Cor.

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Applied Mathematics and Information Sciences