Involutions avoiding the class of permutations in S κ with prefix 12

W. M.B. Dukes, Toufik Mansour

Research output: Contribution to conferencePaperpeer-review

Abstract

An involution π is said to be τ-ccontain any subsequence having all the same pairwise comparisons as τ. This paper concerns the enumeration of involutions which avoid a set A κ of subsequences increasing both in number and in length at the same time. Let A κ be the set of all the permutations 12π 3.. π κ. of length k. For κ = 3 the only subsequence in A κ is 123 and the 123-avoiding involutions of length n are enumerated by the central binomial coefficients (n/⌊n/2]). For k = 4 we give a combinatorial explanation that shows the number of involutions of length n avoiding A 4 is the same as the number of symmetric Schröder paths of length n-1. For each k ≥ 3 we determine the generating function for the number of involutions avoiding the subsequences in A κ, according to length, first entry and number of fixed points.

Original languageEnglish
StatePublished - 2007
Event19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China
Duration: 2 Jul 20076 Jul 2007

Conference

Conference19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
Country/TerritoryChina
CityTianjin
Period2/07/076/07/07

Keywords

  • Forbidden subsequences
  • Involutions
  • Schröder paths
  • Symmetric Schröder paths

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Involutions avoiding the class of permutations in S κ with prefix 12'. Together they form a unique fingerprint.

Cite this