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Parallel and sequential dynamics of two discrete models of signed integer partitions

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  • Chiaselotti, G.
  • Gentile, T.
  • Oliverio, P.A.

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.

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  • Chiaselotti, G. & Gentile, T. & Oliverio, P.A., 2014. "Parallel and sequential dynamics of two discrete models of signed integer partitions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1249-1261.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:1249-1261
    DOI: 10.1016/j.amc.2014.01.118
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    References listed on IDEAS

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    1. G. Chiaselotti & G. Marino & C. Nardi, 2012. "A Minimum Problem for Finite Sets of Real Numbers with Nonnegative Sum," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, May.
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    1. Chiaselotti, G. & Gentile, T. & Infusino, F. & Oliverio, P.A., 2018. "Dependency and accuracy measures for directed graphs," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 781-794.
    2. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Dynamical attraction in parallel network models," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 874-888.
    3. Juan A. Aledo & Ali Barzanouni & Ghazaleh Malekbala & Leila Sharifan & Jose C. Valverde, 2020. "On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    4. Sanahuja, Silvia M., 2016. "New rough approximations for n-cycles and n-paths," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 96-108.
    5. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2017. "On the Periods of Parallel Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-6, January.
    6. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2019. "Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems," Complexity, Hindawi, vol. 2019, pages 1-10, March.
    7. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2020. "Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    8. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Solution to the predecessors and Gardens-of-Eden problems for synchronous systems over directed graphs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 22-28.

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