Using homological duality in consecutive pattern avoidance

Anton Khoroshkin, Boris Shapiro

Research output: Contribution to journalArticlepeer-review


Using the approach suggested in [2] we present a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential generating functions for the number of permutations avoiding elements of these collections as consecutive patterns. In short, the coincidence of the latter generating functions is guaranteed by a length-preserving bijection of patterns in these collections which is identical on the overlappings of pairs of patterns where the overlappings are considered as unordered sets. Our proof is based on a direct algorithm for the computation of the inverse generating functions. As an application we present a large class of patterns where this algorithm is fast and, in particular, allows us to obtain a linear ordinary differential equation with polynomial coefficients satisfied by the inverse generating function.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalElectronic Journal of Combinatorics
Issue number2
StatePublished - 2011
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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