Subgroups of finite soluble groups inducing the same permutation character

In this paper there are found necessary and sufficient conditions that a pair of solvable finite groups, say and , must satisfy for the existence of a solvable finite group containing two isomorphic copies of and inducing the same permutation character. Also a construction of is given as an iterated wreath product, with respect to their actions on their natural modules, of finite one-dimensional affine groups.

     

An efficient image encryption scheme using gray code based permutation approach

In recent years, the operation efficiency of chaos-based image cryptosystems has drawn much more concerns. However, the workload arised from floating point arithmetic in chaotic map iteration prevents the efficiency promotion of these cryptosystems. In this paper, we present a novel image encryption scheme using Gray code based permutation approach. The new permutation strategy takes full advantage of (n, p, k)-Gray-code achievements, and is performed with high efficiency. A plain pixel-related image diffusion scheme is introduced to compose a complete cryptosystem. Simulations and extensive security analyses have been carried out and the results demonstrate the high security and operation efficiency of the proposed scheme.     

New permutation statistics: Variation and a variant

For each permutation π we introduce the variation statistic of π, as the total number of elements on the right between each two adjacent elements of π. We modify this new statistic to get a slightly different variant, which behaves more closely like Mahonian statistics such as maj. In this paper we find an explicit formula for the generating function for the number of permutations of length n according to the variation statistic, and for that according to the modified version.     

A note on the coefficients of inverse polynomials

We describe some relations on the coefficients of a polynomial in terms of the map that induces and use them to characterize the coefficients of the inverse polynomials of some special classes of permutation polynomials.