Some Statistics on Restricted 132 Involutions
نویسندگان
چکیده
منابع مشابه
Restricted 132 - Involutions
We study generating functions for the number of involutions of length n avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary permutation τ of length k. In several interesting cases these generating functions depend only on k and can be expressed via Chebyshev polynomials of the second kind. In particular, we show that involutions of length n avoiding ...
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In this paper we look at polynomials arising from statistics on the classes of involutions, In, and involutions with no fixed points, Jn, in the symmetric group. Our results are motivated by F. Brenti’s conjecture [3] which states that the Eulerian distribution of In is logconcave. Symmetry of the generating functions is shown for the statistics d, maj and the joint distribution (d, maj). We sh...
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Define I n(α) to be the set of involutions of {1, 2, . . . , n} with exactly k fixed points which avoid the pattern α ∈ Si, for some i ≥ 2, and define I n(∅;α) to be the set of involutions of {1, 2, . . . , n} with exactly k fixed points which contain the pattern α ∈ Si, for some i ≥ 2, exactly once. Let in(α) be the number of elements in I k n(α) and let i k n(∅;α) be the number of elements in...
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متن کاملRestricted 132-avoiding permutations
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
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2002
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s000260200009