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.
Bibliographical noteFunding 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