Related papers: A Note on the Classification of Permutation Matrix

We investigate a family of permutation polynomials of finite fields of characteristic 2. Through a connection between permutation polynomials and quadratic forms, a general treatment is presented to characterize these permutation…

We discuss a triangulated category of graded matrix factorizations of a deformed polynomial associated to the $A_{\mu}\textrm{-}$singularity. The semi-universal deformation of the $A_{\mu}\textrm{-}$singularity is given by a certain…

In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…

Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…

We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.

Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…

An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.

We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes.…

This is a survey on permutation classes for the upcoming book Handbook of Enumerative Combinatorics.

This paper addresses various questions about pairs of similarity classes of matrices which contain commuting elements. In the case of matrices over finite fields, we show that the problem of determining such pairs reduces to a question…

This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…

Permutation matrices play an important role in understand the structure of magic squares. In this work, we use a class of symmetric permutation matrices than can be used to categorize magic squares. Many magic squares with a high degree of…

If every element of a matrix group is similar to a permutation matrix, then it is called a permutation-like matrix group. References [4] and [5] showed that, if a permutation-like matrix group contains a maximal cycle of length equal to a…

The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row…

We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.

A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

This paper investigates a novel connection between reductions of companion matrices associated with a symmetric family of certain binomial ideals in the coordinate ring of affine n-space and permutation matrices. Specifically, for fixed…

Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear…