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Combinatorica

, Volume 28, Issue 4, pp 385–400 | Cite as

Decomposing simple permutations, with enumerative consequences

  • Robert Brignall
  • Sophie Huczynska
  • Vincent Vatter
Article

Abstract

We prove that every sufficiently long simple permutation contains two long almost disjoint simple subsequences, and then we show how this result has enumerative consequences. For example, it implies that, for any r, the number of permutations with at most r copies of 132 has an algebraic generating function (this was previously proved, constructively, by Bóna and (independently) Mansour and Vainshtein).

Mathematics Subject Classification (2000)

05D99 05A15 06A07 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Robert Brignall
    • 1
  • Sophie Huczynska
    • 2
  • Vincent Vatter
    • 2
  1. 1.Department of MathematicsUniversity of BristolBristolUK
  2. 2.School of Mathematics and StatisticsUniversity of St Andrews Mathematical InstituteFifeUK

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