Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials

Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243 and 2143. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid 1243, 2143, and certain a...

A ug 2 00 2 Permutations Which Avoid 1243 and 2143 , Continued Fractions , and Chebyshev Polynomials ∗

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243 and 2143. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid 1243, 2143, and certain a...

Restricted Permutations, Continued Fractions, and Chebyshev Polynomials

Let fr n(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12 . . . k, and let Fr(x; k) and F (x, y; k) be the generating functions defined by Fr(x; k) = P n>0 f r n(k)x n and F (x, y; k) = P r>0 Fr(x; k)y r. We find an explicit expression for F (x, y; k) in the form of a continued fraction. This allows us to express Fr(x; k) for 1 6 r 6 k via Cheb...

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

We say that a permutation is a Motzkin permutation if it avoids 132 and there do not exist a <b such that a < b < b+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 distribut...

0 Restricted Permutations , Continued Fractions , and Chebyshev Polynomials