منابع مشابه
Pattern Avoidance in Coloured Permutations
Let Sn be the symmetric group, Cr the cyclic group of order r, and let S (r) n be the wreath product of Sn and Cr; which is the set of all coloured permutations on the symbols 1, 2, . . . , n with colours 1, 2, . . . , r, which is the analogous of the symmetric group when r = 1, and the hyperoctahedral group when r = 2. We prove, for every 2letter coloured pattern φ ∈ S 2 , that the number of φ...
متن کاملPattern Avoidance in Partial Permutations
Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length n with k holes is a sequence of symbols π = π1π2 · · · πn in which each of the symbols from the set {1, 2, . . . , n− k} appears exactly once, while the remaining k symbols of π are “holes”. A. Claesson, V. Jeĺınek and S. Kitaev were supported by the Icelandic Re...
متن کاملPattern Avoidance in Multiset Permutations: Bijective Proof
A permutation σ = σ1σ2 . . . σn of n letters contains the pattern τ = τ1τ2 . . . τk of k letters if for some i1 < i2 < · · · < ik we have σis < σit whenever τs < τt. A permutation is said to avoid any pattern it does not contain. It is well-known that the number of permutations of n letters that avoid a pattern τ of 3 letters is independent of τ . Savage and Wilf [3] have shown the same result ...
متن کاملPattern avoidance in partial permutations ( extended abstract )
Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length n with k holes is a sequence of symbols π = π1π2 · · ·πn in which each of the symbols from the set {1, 2, . . . , n− k} appears exactly once, while the remaining k symbols of π are “holes”. We introduce pattern-avoidance in partial permutations and prove that mos...
متن کاملPattern avoidance in compositions and multiset permutations
One of the most arresting phenomena in the theory of pattern avoidance by permutations is the fact that the number of permutations of n letters that avoid a pattern π of 3 letters is independent of π. In this note we exhibit two generalizations of this fact, to ordered partitions, a.k.a. compositions, of an integer, and to permutations of multisets. It is remarkable that the conclusions are in ...
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ژورنال
عنوان ژورنال: Order
سال: 2015
ISSN: 0167-8094,1572-9273
DOI: 10.1007/s11083-015-9367-7