Partially 2-colored permutations and the Boros–Moll polynomials
نویسندگان
چکیده
منابع مشابه
Restricted colored permutations and Chebyshev polynomials
Several authors have examined connections between restricted permutations and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for colored permutations. First we define a distinguished set of length two and length three patterns, which contains only 312 when just one color is used. Then we give a recursive procedure for computing the generating functio...
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.
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In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the generating function of the fmajk indices of colored permutations. The second result is a combinatorial treatment of a relation on the q-derangement numbers ...
متن کاملOn the Group of Alternating Colored Permutations
The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product Zr ≀Sn. We present a ‘Coxeterlike’ presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of Z r 2 ≀ Sn and use this point of view to give another expression for the length function. ...
متن کاملOn the Excedance Sets of Colored Permutations
We define the excedence set and the excedance word on Gr,n, generalizing a work of Ehrenborg and Steingrimsson and use the inclusion-exclusion principle to calculate the number of colored permutations having a prescribed excedance word. We show some symmetric properties as Log concavity and unimodality of a specific sequence of excedance words.
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2012
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-011-9359-1