Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials

Sergi Elizalde, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


We say that a permutation π is a Motzkin permutation if it avoids 132 and there do not exist a<b such that πa<πb<πb+1. We study the distribution of several statistics in Motzkin permutations, including the length of the longest increasing and decreasing subsequences and the number of rises and descents. We also enumerate Motzkin permutations with additional restrictions, and study the distribution of occurrences of fairly general patterns in this class of permutations.

Original languageEnglish
Pages (from-to)170-189
Number of pages20
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 6 Dec 2005

Bibliographical note

Funding Information:
We would like to thank Marc Noy for helpful comments and suggestions. The first author was partially supported by a MAE fellowship.


  • Chebyshev polynomial
  • Generalized pattern
  • Motzkin path
  • Motzkin permutation
  • Permutation statistic
  • Restricted permutation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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