On non-squashing partitions

N. J.A. Sloane, James Allen Sellers

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Abstract

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 parts, with a specified number of parts, or with a specified maximal part. We use the results to solve a certain box-stacking problem.

Original languageEnglish (US)
Pages (from-to)259-274
Number of pages16
JournalDiscrete Mathematics
Volume294
Issue number3
DOIs
StatePublished - May 6 2005

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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    Sloane, N. J. A., & Sellers, J. A. (2005). On non-squashing partitions. Discrete Mathematics, 294(3), 259-274. https://doi.org/10.1016/j.disc.2004.11.014