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...

Pin showed that every p-state automaton (p a prime) containing a cyclic permutation and a non-permutation has a synchronizing word of length at most (p− 1). In this paper we consider permutation automata with the property that adding any non-permutation will lead to a synchronizing word and establish bounds on the lengths of such synchronizing words. In particular, we show that permutation grou...

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...

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.

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 ...

The VMPC function is a combination of triple permutation composition and integer addition. It differs from a simple triple permutation composition with one integer addition operation performed on some of the elements of the permutation. The consequence of this addition operation is corruption of cycle structure of the transformed permutation the fundamental source of the function's resistance t...

A coloring of a graph G is an assignment of colors to its vertices so that no two adjacent vertices have the same color. We study the problem of coloring permutation graphs using certain properties of the lattice representation of a permutation and relationships between permutations, directed acyclic graphs and rooted trees having speci/c key properties. We propose an e0cient parallel algorithm...