Restricted set of patterns, continued fractions, and Chebyshev polynomials

2001/08/06 by Toufik Mansour, T. Mansour, Mansour, T.
Mathematics · #05A05 #05A15 #30B70 #42C05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05A05 #msc:05A15 #msc:30B70 #msc:42C05

paper · pdf · doi:10.48550/arxiv.math/0108043

9 pages

arxiv created 2001/08/06 · openalex publication_date 2001/08/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study generating functions for the number of permutations in S_n subject to set of restrictions. One of the restrictions belongs to S₃, while the others to S_k. It turns out that in a large variety of cases the answer can be expressed via continued fractions, and Chebyshev polynomials of the second kind.

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