A pattern occurs in a permutation if there is a subsequence of the permutation with the same relative order as the pattern. For mathematical analysis of permutation patterns, strong Wilf-equivalence has been defined as the equivalence between permutation patterns based on the number of occurrences of a pattern. In this paper, we present an algorithm for generating permutations of length n in wh...

This study introduces a method for generating a particular permutation P of a given size N out of N! permutations from a given key. This method computes a unique permutation for a specific size since it takes the same key; therefore, the same permutation can be computed each time the same key and size are applied. The name of random permutation comes from the fact that the probability of gettin...

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...

Connected bipartite permutation graphs without vertex labels are investigated. First, the number of connected bipartite permutation graphs of n vertices is given. Based on the number, a simple algorithm that generates a connected bipartite permutation graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected bipartite permutation graphs is proposed....

We say a permutation π contains or involves the permutation σ if deleting some of the entries of π gives a permutation that is order isomorphic to σ, and we write σ ¤ π. For example, 534162 contains 321 (delete the values 4, 6, and 2). A permutation avoids a permutation if it does not contain it. This notion of containment defines a partial order on the set of all finite permutations, and the d...

Skull can be interpreted as an investigation by PD James into the way a classical detective character, stereotypes, crime and setting would be affected by the introduction of modern-world issues and values. Essentially she has placed the manor-house setting within contemporary Britain, and migrated its inhabitants to Courcy Castle as a controlled experiment in sociology. In this way, James succ...

In this paper, by using a powerful criterion for permutation polynomials given by Zieve, we give several classes of complete permutation monomials over Fqr . In addition, we present a class of complete permutation multinomials, which is a generalization of recent work. Index Terms Finite field, Complete permutation polynomials, Walsh transform, Niho exponents.

There has been a good deal of work in the last decade or so on computing upper bounds of irreducible character values for finite simple groups [G1, G2, GM, LS2, LP, MS-P, R]. Some of this work concerns permutation groups, some groups of Lie type. Some is aimed at worst-case behavior, some at the character values of typical or at least fairly well-behaved elements. Various applications have been...

A modular theory for permutation representations and their centralizer rings is presented, analogous in several respects to the classical work of Brauer on group algebras. Some principal ingredients of the theory are characters of indecomposable components of the permutation module over a p-adic ring, modular characters of the centralizer ring, and the action of normalizers of p-subgroups P on ...

Several permutation strategies are often possible for tests of individual terms in analysis-of-variance (ANOVA) designs. These include restricted permutations, permutation of whole groups of units, permutation of some form of residuals or some combination of these. It is unclear, especially for complex designs involving random factors, mixed models or nested hierarchies, just which permutation ...