Restricted 132-Involutions and Chebyshev Polynomials

2002/01/15 by Olivier Guibert, O. Guibert, Guibert, O. +3
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0201136

18 pages, 1 figure

arxiv created 2002/01/15 · openalex publication_date 2002/01/15 · 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 involutions in S_n avoiding (or containing once) 132, and avoiding (or containing once) an arbitrary permutation τ on k letters. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. In particular, we establish that involutions avoiding both 132 and 12... k have the same enumerative formula according to the length than involutions avoiding both 132 and any \em double-wedge pattern possibly followed by fixed points of total length k. Many results are also shown with a combinatorial point of view.

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