Spectral Properties of Some Combinatorial Matrices

In this paper we investigate the spectra and related questions for various combinatorial matrices, generalizing work by Carlitz, Cooper and Kennedy

Recurrences for Entries of Powers of Matrices

In this note, giving course to a challenge in a recent paper of Larcombe [2], we find the entries of any nth power of a 3 x 3 matrix, and as a byproduct, we recover Larcombe's result on 2 x 2 matrices. Further, we look at block matrices and show an invariance result for the powers of such matrices

On the carlitz rank of permutation polynomials over finite fields:recent developments

The Carlitz rank of a permutation polynomial over a finite field Fq is a simple concept that was introduced in the last decade. In this survey article, we present various interesting results obtained by the use of this notion in the last few years. We emphasize the recent work of the authors on the permutation behavior of polynomials f + g, where f is a permutation over Fq of a given Carlitz rank, and g∈Fq[x] is of prescribed degree. The relation of this problem to the well-known Chowla–Zassenhaus conjecture is described. We also present some initial observations on the iterations of a permutation polynomial f∈Fq[x] and hence on the order of f as an element of the symmetric group S q