✦ LIBER ✦

Permutations of a Multiset Avoiding Permutations of Length 3

✍ Scribed by M.H. Albert; R.E.L. Aldred; M.D. Atkinson; C. Handley; D. Holton

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 107 KB
Volume: 22
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2001.0538

No coin nor oath required. For personal study only.

✦ Synopsis

We consider permutations of a multiset which do not contain certain ordered patterns of length 3. For each possible set of patterns we provide a structural description of the permutations avoiding those patterns, and in many cases a complete enumeration of such permutations according to the underlying multiset.

📜 SIMILAR VOLUMES

On the Number of Permutations Avoiding a

On the Number of Permutations Avoiding a Given Pattern

✍ Noga Alon; Ehud Friedgut 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 118 KB

Let \_ # S k and { # S n be permutations. We say { contains \_ if there exist Stanley and Wilf conjectured that for any \_ # S k there exists a constant c=c(\_) such that F(n, \_) c n for all n. Here we prove the following weaker statement: For every fixed \_ # S k , F(n, \_) c n#\* (n) , where c=c

An Equipartition Property for the Distri

An Equipartition Property for the Distribution of Multiset Permutation Inversions

✍ S. Brunetti; A. Del Lungo; F. Del Ristoro 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 91 KB

The purpose of this paper is to present some enumerative results concerning the class k of permutations of the multiset 1 m 1 2 m 2 r m r having inversion number congruent to k modulo n, with n = m 1 + m 2 + • • • + m r and 0 ≤ k < n. We show that the enumeration of this family of permutations is co

Multiset Permutations and Loopless Gener

Multiset Permutations and Loopless Generation of Ordered Trees with Specified Degree Sequence

✍ James F. Korsh; Paul LaFollette 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 131 KB

An ordered tree with specified degree sequence and n internal nodes has a i Ž . nodes of degree i, where a s 1 q Ý i y 1 a and n s Ý a . This paper presents the first loopless algorithm for generating all ordered trees with specified degree sequence. It uses a new version of the algorithm for gener

A Representation of Even Permutations

✍ L. Cangelmi; P. Cellini 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 80 KB

We give a combinatorial proof of the formula giving the number of representations of an even permutation σ in S n as a product of an n-cycle by an (n -2)-cycle, such a number being (nχ(σ ))(n -3)!, where χ(σ ) is the number of fixed points of σ . This proof relies on the fact that any odd permutatio

Permutations Restricted by Two Distinct

Permutations Restricted by Two Distinct Patterns of Length Three

✍ Aaron Robertson 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 151 KB

Theorem 4.3. For α β ∈ 132 213 213 132 231 312 312, 231 we have s n α β = n2 n-5 for n ≥ 4 and s 3 α β = 1.

Permutability Class of a Semigroup

✍ Andrzej Kisielewicz 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 133 KB

## Given a permutation x n ∈ S. Various permutability conditions were considered for special classes of permutations. We define the permutability class of a semigroup S to be the infinite sequence The aim of this paper is to give a description of such sequences, which generalizes a number of old