A Generalization of the Simion-schmidt Bijection for Restricted Permutations
نویسنده
چکیده
We consider the two permutation statistics which count the distinct pairs obtained from the last two terms of occurrences of patterns τ1 · · · τm−2m(m − 1) and τ1 · · · τm−2(m − 1)m in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution over the symmetric group. As special case we derive a one-to-one correspondence between permutations which avoid each of the patterns τ1 · · · τm−2m(m − 1) ∈ Sm and such ones which avoid each of the patterns τ1 · · · τm−2(m − 1)m ∈ Sm. For m = 3, this correspondence coincides with the bijection given by Simion and Schmidt in their famous paper on restricted permutations.
منابع مشابه
A Generalization of Simion-Schmidt's Bijection for Restricted Permutations
We consider the two permutation statistics which count the distinct pairs obtained from the final two terms of occurrences of patterns τ1 · · · τm−2m(m − 1) and τ1 · · · τm−2(m − 1)m in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution over the symmetric group. As a special case we derive a one-to-one correspondence between...
متن کاملEnumeration formulæ for pattern restricted Stirling permutations
We classify k-Stirling permutations avoiding a set of ordered patterns of length three according to Wilf-equivalence. Moreover, we derive enumeration formulæ for all of the classes using a variety of techniques such as the kernel method, a bijection related to a classical result of Simion and Schmidt, and also structural decompositions of k-Stirling permutations via the so-called block decompos...
متن کاملFast Generation of Fibonacci Permutations
In 1985, Simion and Schmidt showed that |Sn(τ3)|, the cardinality of the set of all length n permutations avoiding the patterns τ3 = {123, 213, 132} is the Fibonacci numbers, fn+1. They also developed a constructive bijection between the set of all binary strings with no two consecutive ones and Sn(τ3). In May 2004, Egge and Mansour generalized this SimionSchmidt counting result and showed that...
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 کاملClassification of Bijections between 321- and 132-avoiding Permutations
It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs of this fact. It turns out that some of the published bijections can easily be obtained from others. In this paper we describe all bijections we were able to find in the literatur...
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:
دوره شماره
صفحات -
تاریخ انتشار 1963