Restricted 132-avoiding k-ary words, Chebyshev polynomials, and continued fractions

Research output: Contribution to journalArticlepeer-review


We study generating functions for the number of n-long k-ary words that avoid both 132 and an arbitrary ℓ-ary pattern. In several interesting cases the generating function depends only on ℓ and is expressed via Chebyshev polynomials of the second kind and continued fractions.

Original languageEnglish
Pages (from-to)175-193
Number of pages19
JournalAdvances in Applied Mathematics
Issue number2
StatePublished - Feb 2006

Bibliographical note

Funding Information:
This work was supported in part by The Center for Computational Mathematics and Scientific Computation (CCMSC), University of Haifa, Israel.


  • Chebyshev polynomials
  • Continued fractions
  • Forbidden subsequence
  • Restricted k-ary words
  • k-ary words

ASJC Scopus subject areas

  • Applied Mathematics


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