Geodesic
Permutations which avoid 1243 and 2143, continued fractions, and Chebyshev polynomials
The electronic journal of combinatorics, Permutation Patterns, Tome 9 (2002) no. 2
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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.
DOI : 10.37236/1679
Classification : 05A05, 05A15, 30B70, 42C05
Mots-clés : restricted permutation, pattern-avoiding permutation, forbidden subsequence, continued fraction, Chebyshev polynomial, enumerations, generating functions 
@article{10_37236_1679,
     author = {Eric S. Egge and Toufik Mansour},
     title = {Permutations which avoid 1243 and 2143, continued fractions, and {Chebyshev} polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     number = {2},
     doi = {10.37236/1679},
     zbl = {1020.05003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1679/}
}
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Eric S. Egge; Toufik Mansour. Permutations which avoid 1243 and 2143, continued fractions, and Chebyshev polynomials. The electronic journal of combinatorics, Permutation Patterns, Tome 9 (2002) no. 2. doi: 10.37236/1679

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