Chiaselotti, G.; Marino, G.; Oliverio, P. A.; Petrassi, D. A discrete dynamical model of signed partitions. (English) Zbl 1266.06001 J. Appl. Math. 2013, Article ID 973501, 10 p. (2013). Summary: We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems. Cited in 5 Documents MSC: 06A07 Combinatorics of partially ordered sets 05D99 Extremal combinatorics PDFBibTeX XMLCite \textit{G. Chiaselotti} et al., J. Appl. Math. 2013, Article ID 973501, 10 p. (2013; Zbl 1266.06001) Full Text: DOI References: [1] D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems, Cambridge University Press, Cambridge, UK, 1990. · Zbl 0702.58002 [2] J. L. G. Guirao, F. L. Pelayo, and J. C. Valverde, “Modeling the dynamics of concurrent computing systems,” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1402-1406, 2011. · Zbl 1217.68150 [3] W. Foryś, J. L. G. Guirao, and P. Oprocha, “A dynamical model of parallel computation on bi-infinite time-scale,” Journal of Computational and Applied Mathematics, vol. 235, no. 7, pp. 1826-1832, 2011. · Zbl 1214.68247 [4] J. A. Aledo, S. Martínez, and J. C. Valverde, “Parallel dynamical systems over directed dependency graphs,” Applied Mathematics and Computation, vol. 219, no. 3, pp. 1114-1119, 2012. · Zbl 1291.37018 [5] J. A. Aledo, S. Martinez, and J. C. Valverde, “Parallel discrete dynamical systems on independent local functions,” Journal of Computational and Applied Mathematics, vol. 237, no. 1, pp. 335-339, 2013. · Zbl 1248.37077 [6] J. A. Aledo, S. Martínez, F. L. Pelayo, and J. C. Valverde, “Parallel discrete dynamical systems on maxterm and minterm Boolean functions,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 666-671, 2012. · Zbl 1255.37003 [7] C. Bisi and G. Chiaselotti, “A class of lattices and boolean functions related to the Manickam-Miklös-Singhi conjecture,” Advances in Geometry, vol. 13, no. 1, pp. 1-27, 2013. · Zbl 1259.05178 [8] G. E. Andrews, “Euler’s ‘De Partitio numerorum’,” Bulletin of American Mathematical Society, vol. 44, no. 4, pp. 561-573, 2007. · Zbl 1172.11031 [9] W. J. Keith, “A bijective toolkit for signed partitions,” Annals of Combinatorics, vol. 15, no. 1, pp. 95-117, 2011. · Zbl 1233.05031 [10] G. Chiaselotti, G. Marino, and C. Nardi, “A minimum problem for finite sets of real numbers with nonnegative sum,” Journal of Applied Mathematics, vol. 2012, Article ID 847958, 15 pages, 2012. · Zbl 1273.11045 [11] T. Brylawski, “The lattice of integer partitions,” Discrete Mathematics, vol. 6, pp. 201-219, 1973. · Zbl 0283.06003 [12] K. J. Al-Agha and R. J. Greechie, “The involutory dimension of involution posets,” Order, vol. 18, no. 4, pp. 323-337, 2002. · Zbl 0993.03082 [13] K. Brenneman, R. Haas, and A. G. Helminck, “Implementing an algorithm for the twisted involution poset for Weyl groups,” in Proceedings of the 37th Southeastern International Conference on Combinatorics, Graph Theory and Computing, vol. 182, pp. 137-144, 2006. · Zbl 1112.20033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.