Decomposing simple permutations, with enumerative consequences

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).

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Correspondence to Vincent Vatter.

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Supported by a Royal Society Dorothy Hodgkin Research Fellowship.

Supported by EPSRC grant GR/S53503/01.

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Brignall, R., Huczynska, S. & Vatter, V. Decomposing simple permutations, with enumerative consequences. Combinatorica 28, 385–400 (2008). https://doi.org/10.1007/s00493-008-2314-0

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Mathematics Subject Classification (2000)

  • 05D99
  • 05A15
  • 06A07