On Non-Squashing Partitions
组合数学
2014-09-17 v1
摘要
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.
引用
@article{arxiv.math/0312418,
title = {On Non-Squashing Partitions},
author = {N. J. A. Sloane and James A. Sellers},
journal= {arXiv preprint arXiv:math/0312418},
year = {2014}
}
备注
15 pages, 2 figs