Permutation Patterns and Cell Decompositions

Toufik Mansour, Matthias Schork

Research output: Contribution to journalArticlepeer-review


Let Sn be the symmetric group of all permutations of n letters, and let Sn(T) be the set of those permutations which avoid a given set of patterns T. In the present paper, we consider a τ-reduction argument where τ∈ Sm is given and all patterns in T are assumed to contain τ. For these situations, cell decompositions are introduced and studied. We describe an observation which allows to reduce the determination of the generating function for | Sn(T) | to the determination of a set of generating functions for simpler problems. The usefulness of this approach is demonstrated by several examples.

Original languageEnglish
Pages (from-to)169-183
Number of pages15
JournalMathematics in Computer Science
Issue number1-2
StatePublished - 1 Jun 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.


  • Pattern avoidance
  • Permutation
  • Wilf-equivalence

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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