Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials

Details Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials

2002-08-06

arxiv.org/abs/math/0208046v1

Mathematics

Combinatorics

32 pages, 4 figures

Scientific paper

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243 and 2143. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid 1243, 2143, and certain additional patterns. We also give generating functions for permutations which avoid 1243 and 2143 and contain certain additional patterns exactly once. In all cases we express these generating functions in terms of Chebyshev polynomials of the second kind.

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