Integrals, partitions and MacMahon's Theorem

George E. Andrews, Henrik Eriksson, Fedor Petrov, Dan Romik

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of applications. The object of this paper is to extend that study in various ways. First, the relationship of partitions with no consecutive integers to a theorem of MacMahon and mock theta functions is explored independently. Secondly, we derive in a succinct manner a relevant definite integral related to the asymptotic enumeration of partitions with short sequences. Finally, we provide the generating function for partitions with no sequences of length K and part exceeding N.

Original languageEnglish (US)
Pages (from-to)545-554
Number of pages10
JournalJournal of Combinatorial Theory. Series A
Volume114
Issue number3
DOIs
StatePublished - Apr 1 2007

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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