Restricted Permutations, Continued Fractions, and Chebyshev Polynomials

0 Restricted Permutations , Continued Fractions , and Chebyshev Polynomials

Horse paths, restricted 132-avoiding permutations, continued fractions, and Chebyshev polynomials

Several authors have examined connections among 132-avoiding permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we find analogues for some of these results for permutations π avoiding 132 and 1223 (there is no occurrence πi < πj < πj+1 such that 1 ≤ i ≤ j − 2) and provide a combinatorial interpretation for such permutations in terms of lattice paths. ...

ul 2 00 3 Restricted 3412 - Avoiding Involutions : Continued Fractions , Chebyshev Polynomials and Enumerations ∗

Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to gi...

O ct 2 00 6 RESTRICTED MOTZKIN PERMUTATIONS , MOTZKIN PATHS , CONTINUED FRACTIONS , AND CHEBYSHEV POLYNOMIALS

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

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...

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...