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Arithmetic Properties of Non-Squashing Partitions into Distinct Parts

Authors:	Email author" target="_blank">?ystein?J?R?dseth Email author James?A?Sellers Kevin?M?Courtright

Institution:	(1) Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, 5008 Bergen, Norway;(2) Department of Mathematics, Penn State University, University Park, PA 16802, USA

Abstract:	A partition $n = p_1 + p_2 + \cdots + p_k$ with $1 \leq p_1 \leq p_2 \leq \cdots \leq p_k$ is non-squashing if $p_1 + \cdots + p_j \leqslant p_{j + 1} {\text{for}}1 \leqslant j \leqslant k - 1.$ On their way towards the solution of a certain box-stacking problem, Sloane and Sellers were led to consider the number b(n) of non-squashing partitions of n into distinct parts. Sloane and Sellers did briefly consider congruences for b(n) modulo 2. In this paper we show that 2^r-2 is the exact power of 2 dividing the difference b(2^r+1n)–b(2^r-1n) for n odd and r 2.

Keywords:	05A17 11P83
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