2003/07/03 by Eric S. Egge, Egge, Eric S.
Mathematics · Physics and Astronomy · #05A05 #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0307050
26 pages
arxiv created 2003/07/03 · openalex publication_date 2003/07/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to give enumerations and generating functions for involutions which avoid 3412 and various sets of additional patterns. In many cases we express these generating functions in terms of Chebyshev polynomials of the second kind.