Restricted 1-3-2 Permutations and Generalized Patterns |
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Authors: | Toufik Mansour |
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Institution: | LaBRI, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France, e-mail: toufik@labri.fr, FR
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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 t \tau on k letters, or containing t \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. |
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