Restricted Motzkin Permutations, Motzkin Paths,
Continued Fractions, and Chebyshev Polynomials
 

Toufik Mansour

Department of Mathematics, Haifa University, 31905 Haifa, Israel  

toufik@math2.haifa.ac.il
 

Abstract.      Full Text PDF

We say that a permutation  is a Motzkin permutation if it avoids  and there do not exist  such that . 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.