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Layered Restrictions and Chebyshev Polynomials
Toufik Mansour1 and Alek Vainshtein2
1LaBRI, University Bordeaux 1, 351 cours de la Liberation, 33405 Talence Cedex, France
toufik@labri.fr
2Department of Mathematics and Department of Computer Science, University of Haifa, Haifa,Israel 31905
alek@mathcs.haifa.ac.il
Annals of Combinatorics 5 (3) p.451-458 September, 2001
AMS Subject Classification: 05A05, 05A15, 30B70, 42C05
Abstract:
A permutation is called layered if it consists of the disjoint union of substrings (layers) so that the entries decrease within each layer, and increase between the layers. We find the generating function for the number of permutations on n letters avoiding (1,2,3) and a layered permutation on k letters. In the most interesting case of two layers, the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind.
Keywords: permutations, pattern avoidance, enumeration, generating functions, Chebyshev polynomials

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