. C O ] 2 6 Ju n 20 01 RESTRICTED PERMUTATIONS AND CHEBYSHEV
نویسندگان
چکیده
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
منابع مشابه
ar X iv : m at h / 01 08 04 3 v 1 [ m at h . C O ] 6 A ug 2 00 1 Restricted set of patterns , continued fractions , and Chebyshev polynomials
We study generating functions for the number of permutations in Sn subject to set of restrictions. One of the restrictions belongs to S3, while the others to Sk. It turns out that in a large variety of cases the answer can be expressed via continued fractions, and Chebyshev polynomials of the second kind. 2001 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 کامل2 00 2 Restricted Permutations and Chebyshev Polynomials
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.
متن کامل6 D ec 1 99 9 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) = ∑ n>0 f r n (k)xn and F (x, y; k) = ∑ r>0 Fr(x; k)y r . We find an explcit 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 Che...
متن کاملRestricted 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...
متن کامل