On Non-Squashing Partitions

Details On Non-Squashing Partitions On Non-Squashing Partitions

2003-12-22

arxiv.org/abs/math/0312418v1

Mathematics

Combinatorics

15 pages, 2 figs

Scientific paper

A partition n = p_1 + p_2 + ... + p_k with 1 <= p_1 <= p_2 <= ... <= p_k is called non-squashing if p_1 + ... + p_j <= p_{j+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 parts, with a specified number of parts, or with a specified maximal part. We use the results to solve a certain box-stacking problem.

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