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Annals of Combinatorics

, Volume 6, Issue 1, pp 65–76 | Cite as

Restricted 1-3-2 Permutations and Generalized Patterns

  • Toufik Mansour

Abstract.

Recently, Babson and Steingrimsson (see [2]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We study generating functions for the number of permutations on n letters avoiding 1-3-2 (or containing 1-3-2 exactly once) and an arbitrary generalized pattern \( \tau \) on k letters, or containing \( \tau \) exactly once. In several cases, the generating function depends only on k and can be expressed via Chebyshev polynomials of the second kind, and the generating function of Motzkin numbers.

Keywords: restricted permutations, generalized patterns, Chebyshev polynomials 

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Copyright information

© Birkhäuser Verlag Basel, 2002

Authors and Affiliations

  • Toufik Mansour
    • 1
  1. 1.LaBRI, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France, e-mail: toufik@labri.frFR

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