Restricted partitions and q-Pell numbers

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


In this paper, we provide new combinatorial interpretations for the Pell numbers pn in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by pn. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization of pn. Similar considerations using the comajor index statistic yields a further generalization of the q-Pell number studied by Santos and Sills.

Original languageEnglish
Pages (from-to)346-355
Number of pages10
JournalCentral European Journal of Mathematics
Issue number2
StatePublished - 2011


  • Comajor index
  • Inversion
  • Pattern avoidance
  • Pell number
  • q-generalization

ASJC Scopus subject areas

  • General Mathematics


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