Restricted permutations, continued fractions, and Chebyshev polynomials

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Let fnr(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12 . . . k, and let F r(x; k) and F(x, y; k) be the generating functions defined by F r(x; k) = Σn≥0 fnr(k)x n and F(x, y; k) = Σr≥0 Fr(x; k)y r. We find an explicit expression for F(x, y; k) in the form of a continued fraction. This allows us to express Fr(x; k) for 1 ≤ r ≤ k via Chebyshev polynomials of the second kind.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalElectronic Journal of Combinatorics
Issue number1 R
StatePublished - 2000

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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