Restricted ascent sequences and catalan numbers

David Callan, Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


In this paper, we identify all members of the (4,4)-Wilf equivalence class for ascent sequences corresponding to the Catalan number Cn = 1/n+1(2n/n). This extends recent work concerning avoidance of a single pattern and pro-vides apparently new combinatorial interpretations for Cn. In several cases, the subset of the class consisting of those members having exactly m ascents is given by the Narayana number Nn,m+1 = 1/n(n/m+1)(n/m). We conclude by considering a further refinement in the case of avoiding 021.

Original languageEnglish
Pages (from-to)288-303
Number of pages16
JournalApplicable Analysis and Discrete Mathematics
Issue number2
StatePublished - 2014


  • Ascent sequence
  • Catalan number
  • Kernel method
  • Narayana number

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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