This article discusses two new matrix operators constructed differently from and by taking a square matrix's main diagonal supra-diagonal entries. We call these the . explicitly construct that transforms to , where is an for also derive various properties matrix.Keywords— permutation matrix; vecp*; vech*; vec operator

Abstract. This article extracts and analyzes local optima networks for the permutation flow-shop problem. Two widely used move operators for permutation representations, namely, swap and insertion, are incorporated into the network landscape model. The performance of a heuristic search algorithm on this problem is also analyzed. In particular, we study the correlation between local optima netwo...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...

In this paper, we explore the theory and expand upon practice of fitness landscape analysis for optimization problems over space permutations. Many computational analytical tools analysis, such as distance correlation, require identifying a metric measuring similarity different solutions to problem. We begin with survey available metrics permutations, then use principal component classify these...

In this paper we concentrate on Job Shop Scheduling as a representative of constrained combinatorial problems. We introduce a new permutation representation for this problem. Three crossover operators , diierent in tending to preserve the relative order, the absolute order, and the position in the permutation, are deened. By experiment we observe the strongest phenotypical correlation between p...

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.

This is the second in a series of papers which consider the orbifolds of permutation-type as candidates for new physical string systems at higher central charge. In the first paper, I worked out the extended actions of the twisted sectors of those orbifolds – which exhibit new permutation-twisted world-sheet gravities and correspondingly extended diffeomorphism groups. In this paper I begin the...

A permutation with no fixed points is called a derangement.The subset $mathcal{D}$ of a permutation group is derangement if all elements of $mathcal{D}$ are derangement.Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

Classical random walks on finite graphs have an underrated property: a walk from any vertex can reach every other in time, provided they are connected. Discrete-time quantum connected however, infinite hitting times. This phenomenon is related to graph symmetry, as previously characterized by the group of direction-preserving automorphisms that trivially affect coin Hilbert space. If symmetric ...