The ith cycle minor of a permutation p of the set {1, 2, . . . , n} is the permutation formed by deleting an entry i from the decomposition of p into disjoint cycles and reducing each remaining entry larger than i by 1. In this paper, we show that any permutation of {1, 2, . . . , n} can be reconstructed from its set of cycle minors if and only if n ≥ 6. We then use this to provide an alternate...

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...

Two papers in the Journal this month examine patterns of prescribing practice. With established clinical guidelines for the management of individuals with treatment-resistant schizophrenia in mind, Howes et al (pp. 481–485) reviewed prescribing practices prior to commencement of clozapine for a sample of patients managed within one mental health service. The authors found evidence of a signific...

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...

We have previously reported that, depending on their activation status, mouse γδ T cells can either enhance or inhibit the activity of IL-17(+) autoreactive T cells in experimental autoimmune uveitis. In this study, we showed that γδ T cells in naive C57BL/6 (B6) mouse do not express the IL-23R, whereas in immunized mice, it is expressed on >50% of γδ T cells. In vitro studies showed that IL-23...

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.