Results 21 to 30 of about 4,436 (299)
A new algorithm for generating integer partitions and its parallel implementations on CPU and FPGA [PDF]
International Journal of Electronics and TelecommunicationsIn this paper, the long-known bit representation of integer partitions was used in a novel way to develop an algorithm for generating the next partition of an integer n.
Marek Nałęcz, Gustaw Mazurek
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On integer partitions and continued fraction type algorithms [PDF]
Ramanujan Journal, 2023 Wael Baalbaki +4 more
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The lattice of integer partitions
Discrete Mathematics, 1973 AbstractIn this paper we study the lattice Ln of partitions of an integer n ordered by dominance. We show Ln to be isomorphic to an infimum subsemilattice under the component ordering of certain concave nondecreasing (n+1)-tuples. For Ln, we give the covering relation, maximal covering number, minimal chains, infimum and supremum irreducibles, a chain ...
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Some Special Integer Partitions Generated by a Family of Functions
Trends in Computational and Applied Mathematics, 2023 In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define a collection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from
M. L. Matte
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Dynamics of the Picking transformation on integer partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 This paper studies a conservative transformation defined on families of finite sets. It consists in removing one element from each set and adding a new set composed of the removed elements.
Thi Ha Duong Phan, Eric Thierry
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$m$-noncrossing partitions and $m$-clusters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $W$ be a finite crystallographic reflection group, with root system $\Phi$. Associated to $W$ there is a positive integer, the generalized Catalan number, which counts the clusters in the associated cluster algebra, the noncrossing partitions for $W$,
Aslak Bakke Buan +2 more
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On the Distribution of the spt-Crank
Mathematics, 2013 Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any n the sequence {NS (m, n)}m is unimodal, where NS (m, n) is the number of S-partitions of size n with crank m weight by the spt-crank.
Robert C. Rhoades +2 more
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The topology of restricted partition posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $Π ^• _{\vec{c}}$ is a wedge of $β\vec{c}$ spheres of the same dimensions, where $β\vec{c}$ is the number of permutations with descent composition ^$\vec{
Richard Ehrenborg, JiYoon Jung
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Separable integer partition classes
Transactions of the American Mathematical Society, Series B, 2022 A classical method for partition generating function is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n n copies of n n are presented.
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Multisectioned partitions of integers [PDF]
Pacific Journal of Mathematics, 1977 This paper presents identities on generating functions for multisectioned partitions of integers by developing in the language of partitions some powerful and essentially combinatorial techniques from the literature of principal differential ideals. D. Mead has stated in Vol. 42 of this journal that one can obtain interesting combinatorial relations by
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