On Sloane's generalization of non-squashing stacks of boxes

George E. Andrews, James A. Sellers

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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 box stacking problem by obtaining a generating function for the number of such stacks and discuss partition functions which arise via this generating function.

Original languageEnglish (US)
Pages (from-to)1185-1190
Number of pages6
JournalDiscrete Mathematics
Volume307
Issue number9-10
DOIs
StatePublished - May 6 2007

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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