Partitions with fixed differences between largest and smallest parts

George E. Andrews, Matthias Beck, Neville Robbins

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We study the number p(n, t) of partitions of n with difference t between largest and smallest parts. Our main result is an explicit formula for the generating function Pt(q) := ∑n≥1 p(n, t) qn. Somewhat surprisingly, Pt(q) is a rational function for t > 1; equivalently, p(n, t) is a quasipolynomial in n for fixed t > 1. Our result generalizes to partitions with an arbitrary number of specified distances.

Original languageEnglish (US)
Pages (from-to)4283-4289
Number of pages7
JournalProceedings of the American Mathematical Society
Volume143
Issue number10
DOIs
StatePublished - Oct 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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