On non-squashing partitions
نویسندگان
چکیده
منابع مشابه
On non-squashing partitions
A partition n = p1 + p2 + · · · + pk with 1 ≤ p1 ≤ p2 ≤ · · · ≤ pk is called non-squashing if p1 + · · · + pj ≤ pj+1 for 1 ≤ j ≤ k − 1. Hirschhorn and Sellers showed that the number of non-squashing partitions of n is equal to the number of binary partitions of n. Here we exhibit an explicit bijection between the two families, and determine the number of non-squashing partitions with distinct p...
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We define M-sequence non-squashing partitions, which specialize to m-ary partitions Sloane, among others), factorial partitions, and numerous other general partition families of interest. We establish an exact formula, various combinatorial interpretations, as well as the asymptotic growth of M-sequence non-squashing partition functions, functions whose associated generating functions are non-m...
متن کاملInfinite Families of Divisibility Properties modulo 4 for Non–squashing Partitions into Distinct Parts
Abstract In 2005, Sloane and Sellers defined a function b(n) which denotes the number of nonsquashing partitions of n into distinct parts. In their 2005 paper, Sloane and Sellers also proved various congruence properties modulo 2 satisfied by b(n). In this note, we extend their results by proving two infinite families of congruence properties modulo 4 for b(n). In particular, we prove that for ...
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Recently, Sloane and Sellers solved a certain box stacking problem related to non– squashing partitions. These are defined as partitions n = p1 + p2 + · · · + pk with 1 ≤ p1 ≤ p2 ≤ · · · ≤ pk wherein p1 + · · · + pj ≤ pj+1 for 1 ≤ j ≤ k − 1. Sloane has also hinted at a generalized box stacking problem which is closely related to generalized non–squashing partitions. We solve this generalized bo...
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Four statistics, ls, rb, rs, and lb, previously studied on all partitions of { 1, 2, ..., n }, are applied to non-crossing partitions. We consider single and joint distributions of these statistics and prove equidistribution results. We obtain qand p, q-analogues of Catalan and Narayana numbers which refine the rank symmetry and unimodality of the lattice of non-crossing partitions. Two unimoda...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.11.014