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restricted 1-3-2 permutations and generalized patterns

T. Mansour
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Abstract

Recently, Babson and Steingrimsson (see [BS]) 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 $τ$ on $k$ letters, or containing $τ$ exactly once. In several cases the generating function depends only on $k$ and is expressed via Chebyshev polynomials of the second kind, and generating function of Motzkin numbers.

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T. Mansour. 2001-10-03. restricted 1-3-2 permutations and generalized patterns. https://arxiv.org/abs/math/0110039

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