2 00 2 Restricted Permutations and Chebyshev Polynomials
نویسندگان
چکیده
We study generating functions for the number of permutations in S n subject to two restrictions. One of the restrictions belongs to S 3 , while the other belongs to S k. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind.
منابع مشابه
2 A ug 2 00 1 RESTRICTED PERMUTATIONS AND CHEBYSHEV POLYNOMIALS
We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05
متن کاملO 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 ...
متن کاملul 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...
متن کاملA 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...
متن کامل4 O ct 2 00 0 RESTRICTED 132 - AVOIDING
We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05
متن کامل