Permutations Containing A Pattern Exactly Once And Avoiding At Least Two Patterns Of Three Letters
نویسنده
چکیده
In this paper, we find an explicit formulas, or recurrences, in terms of generating functions for the cardinalities of the sets Sn(T ; τ) of all permutations in Sn that contain τ ∈ Sk exactly once and avoid a subset T ⊆ S3 where |T | ≥ 2.
منابع مشابه
Restricted 1-3-2 Permutations and Generalized Patterns
Recently, Babson and Steingrimsson (see [2]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We study generating functions for the number of permutations on n letters avoiding 1-3-2 (or containing 1-3-2 exactly once) and an arbitrary generalized pattern τ on k letters, or containing τ exactly onc...
متن کاملPermutations Avoiding a Pair of Generalized Patterns of Length Three with Exactly One Adjacent Pair of Letters
Abstract. In [1] Babson and Steingŕımsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Claesson [2] presented a complete solution for the number of permutations avoiding any single (generalized) pattern of length three with exactly one adjacent pair of letters. For eight of these twelve pattern...
متن کاملm at h . C O / 0 20 52 06 v 1 1 9 M ay 2 00 2 132 - avoiding Two - stack Sortable Permutations , Fibonacci Numbers , and Pell Numbers ∗
In [W2] West conjectured that there are 2(3n)!/((n+1)!(2n+1)!) two-stack sortable permutations on n letters. This conjecture was proved analytically by Zeilberger in [Z]. Later, Dulucq, Gire, and Guibert [DGG] gave a combinatorial proof of this conjecture. In the present paper we study generating functions for the number of two-stack sortable permutations on n letters avoiding (or containing ex...
متن کاملar X iv : m at h / 02 06 16 9 v 1 [ m at h . C O ] 1 7 Ju n 20 02 SOME STATISTICS ON RESTRICTED 132 INVOLUTIONS
In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding involutions and Dyck word prefixes of same length. Extending this bijection to bilateral words allows to determine more parameters; in particular, we consider the...
متن کاملPermutations containing and avoiding certain patterns
Let T k = {σ ∈ Sk | σ1 = m}. We prove that the number of permutations which avoid all patterns in T k equals (k − 2)!(k − 1) n+1−k for k ≤ n. We then prove that for any τ ∈ T 1 k (or any τ ∈ T k k ), the number of permutations which avoid all patterns in T 1 k (or in T k k ) except for τ and contain τ exactly once equals (n + 1 − k)(k − 1)n−k for k ≤ n. Finally, for any τ ∈ T k , 2 ≤ m ≤ k − 1,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Ars Comb.
دوره 72 شماره
صفحات -
تاریخ انتشار 2004