We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial description of the associated permutation polytope. In the case of three orbits the facet structure is...

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, a new loss-less symmetric image encryption using a permutation and diffusion structure is proposed. A new key generation process generates secondary keys that act as control parameter for permutation order and diffusion bit generator. The Image pixels are scrambled in bit level. Permutation order is generated using the parametric switching type that permutes the pixel in bit wise...

Analysis of molecular variance (AMOVA) is a widely used tool for quantifying the contribution of various levels of population structure to patterns of genetic variation. Implementations of AMOVA use permutation tests to evaluate null hypotheses of no population structure within groups and between groups. With few populations per group, between-group structure might be impossible to detect becau...

P ∈ SN is a fast forward permutation if for each m the computational complexity of evaluating Pm(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in SN is (N) if one does not us...

We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our previous work for vexillary permutations. We also analyze general tilings of Elnitsky’s polygon, and demonstrate that these are closely related to the pattern...

Let G be a transitive permutation group of degree n. We say that G is 2′elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 2′-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate autom...