English

restricted 1-3-2 permutations and generalized patterns

Combinatorics 2007-05-23 v1

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 nn letters avoiding 1321-3-2 (or containing 1321-3-2 exactly once) and an arbitrary generalized pattern τ\tau on kk letters, or containing τ\tau exactly once. In several cases the generating function depends only on kk and is expressed via Chebyshev polynomials of the second kind, and generating function of Motzkin numbers.

Keywords

Cite

@article{arxiv.math/0110039,
  title  = {restricted 1-3-2 permutations and generalized patterns},
  author = {T. Mansour},
  journal= {arXiv preprint arXiv:math/0110039},
  year   = {2007}
}

Comments

10 pages