Recurrence relation with two indices and plane compositions

Arnold Knopfmacher, Toufik Mansour, Augustine Munagi

Research output: Contribution to journalArticlepeer-review


The aim of this paper is to study analytical and combinatorial methods to solve a special type of recurrence relation with two indices. It is shown that the recurrence relation enumerates a natural combinatorial object called a plane composition. In addition, further interesting recurrence relations arise in the study of statistics for these plane compositions.

Original languageEnglish
Pages (from-to)115-127
Number of pages13
JournalJournal of Difference Equations and Applications
Issue number1
StatePublished - 2009


  • Asymptotics
  • Difference equations
  • Generating functions
  • Plane compositions

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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