The enumeration of permutations whose posets have a maximum element

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Recently, Tenner [B.E. Tenner, Reduced decompositions and permutation patterns, J. Algebraic. Combin., in press, preprint arXiv: math.CO/0506242] studied the set of posets of a permutation of length n with unique maximal element, which arise naturally when studying the set of zonotopal tilings of Elnitsky's polygon. In this paper, we prove that the number of such posets is given byP5 n - 4 P5 (n - 1) + 2 P5 (n - 2) - underover(∑, j = 0, n - 2) Cj P5 (n - 2 - j), where Pn is the nth Padovan number and Cn is the nth Catalan number.

Original languageEnglish
Pages (from-to)434-442
Number of pages9
JournalAdvances in Applied Mathematics
Issue number4
StatePublished - Oct 2006


  • Catalan numbers
  • Functional equations
  • Padovan numbers
  • Posets have a maximal element
  • Restricted permutations

ASJC Scopus subject areas

  • Applied Mathematics


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