منابع مشابه
Refined restricted involutions
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...
متن کاملRestricted 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 ...
متن کاملRestricted involutions and Motzkin paths
Given a permutation σ ∈ Sn, one can partition the set {1, 2, . . . , n} into intervals A1, . . . , At such that σ(Aj) = Aj for every j. The restrictions of σ to the intervals in the finest of these decompositions are called connected components of σ. A permutation σ with a single connected component is called connected. Given a permutation σ ∈ Sn, we define the reverse of σ to be the permutatio...
متن کاملRefined Restricted Permutations
Define Sk n(α) to be the set of permutations of {1, 2, . . . ,n} with exactly k fixed points which avoid the pattern α∈ Sm. Let sn(α) be the size of Sk n(α). We investigate S0 n(α) for all α∈ S3 as well as show that sn(132) = s k n(213) = s k n(321) and s k n(231) = s k n(312) for all 0 ≤ k ≤ n.
متن کاملSymmetric Schröder paths and restricted involutions
Let Ak be the set of permutations in the symmetric group Sk with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns Ak. We present a bijection between symmetric Schröder paths of length 2n and involutions of length n + 1 avoiding A4. Statistics such as the number of right-to-left maxima and fixed points of the involution correspond to the number of ste...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2004.09.006