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Abstract: 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 ... (Update)
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BibTeX entry: (Update)
@misc{ egge-permutations,
author = "Eric S. Egge and Toufik Mansour",
title = "Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev
Polynomials",
url = "citeseer.ist.psu.edu/egge03permutations.html" }
Citations (may not include all citations):151 Cambridge University Press (context) - Stanley, volume - 1999
61 Combinatorial aspects of continued fractions (context) - Flajolet - 1980
53 Restricted permutations (context) - Simion, Schmidt - 1985
35 Generating trees and the Catalan and Schroder numbers (context) - West - 1995
26 Permutations with restricted patterns and Dyck paths - Krattenthaler - 2001
26 Generating trees and forbidden subsequences - West - 1996
17 Permutations with forbidden subsequences and a generalized S.. (context) - Kremer - 2000
13 Forbidden subsequences and Chebyshev polynomials - Chow, West - 1999
9 a motifs exclus et cartes planaire: quelques problemes algo.. (context) - Gire, permutations - 1993
9 Permutations avoiding an increasing number of length-increas.. (context) - Barcucci, Lungo et al. - 2000
8 Continued fractions and Catalan problems (context) - Jani, Rieper - 2000
8 and Chebyshev polynomials (context) - Mansour, Vainshtein et al. - 2000
6 Restricted 132-avoiding permutations (context) - Mansour, Vainshtein - 2001
5 Permutation patterns and continued fractions - Robertson, Wilf et al. - 1999
4 Permutations with Forbidden Patterns (context) - Mansour - 2001
4 Restricted permutations and Chebyshev polynomials (context) - Mansour, Vainshtein - 2002
4 the diagram of Schroder permutations - Reifegerste - 2003
4 Catalan continued fractions and increasing subsequences in p.. (context) - Br, Claesson et al. - 2002
4 An area-to-inv bijection between Dyck paths and 312-avoiding.. - Bandlow, Killpatrick - 2001
4 A weight-preserving bijection between Schroder paths and Sc.. (context) - Bandlow, Egge et al.
3 Layered restrictions and Chebyshev polynomials (context) - Mansour, Vainshtein - 2001
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