Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials Original Research Article

We say that a permutation image is a Motzkin permutation if it avoids 132 and there do not exist image such that image. 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.