 Parallel and sequential dynamics of two discrete models of signed integer partitionsG. Chiaselotti, T. Gentile and P.A. Oliverio Applied Mathematics and Computation, 2014, vol. 232, issue C, 1249-1261 Abstract: In this paper we complete and generalize some previous results concerning the computing of the sequential and parallel convergent time for two discrete dynamical system of signed integer partitions. We also refine the concept of parallel convergent time for a finite graded partially ordered set (briefly poset) X which is also a discrete dynamical model. To this aim we define the concept of fundamental sequence of X and we compute this sequence in two particularly important cases. In the first case, when X is the finite lattice S(n,r) of all the signed integer partitions ar,…,a1,b1,…,bn-r such that r⩾ar⩾⋯⩾a1⩾0⩾b1⩾⋯⩾bn-r⩾-(n-r), where n⩾r⩾0 and the unique part that can be repeated is 0. In the second case, when X is the sub-lattice S(n,d,r) of all the signed integer partitions of S(n,r) having exactly d non-zero parts. The relevance of the previous lattices as discrete dynamical models is related to their link with some unsolved extremal combinatorial sum problems. Keywords: Discrete dynamical models; Integer partitions; Sequential and parallel dynamics; Graded lattices (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:1249-1261 DOI: 10.1016/j.amc.2014.01.118 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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