Related papers: A Note on the Classification of Permutation Matrix
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d\times d$ matrix. Motivated by [4], we define a similar class of matrices which are a generalization of…
Two factorizations of a permutation into products of cycles are equivalent if one can be obtained from the other by repeatedly interchanging adjacent disjoint factors. This paper studies the enumeration of equivalence classes under this…
This article introduces an analogue of permutation classes in the context of polyominoes. For both permutation classes and polyomino classes, we present an original way of characterizing them by avoidance constraints (namely, with excluded…
In this paper, we study the occurrence of patterns in the cycle structures of permutations.
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…
This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
A brief presentation of basic definitions and notation used in permutation patterns research.
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.
Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…
In this note, a criterion for a class of binomials to be permutation polynomials is proposed. As a consequence, many classes of binomial permutation polynomials and monomial complete permutation polynomials are obtained. The exponents in…
Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…
Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…
We propose a diagrammatic notation for matrix differentiation. Our new notation enables us to derive formulas for matrix differentiation more easily than the usual matrix (or index) notation. We demonstrate the effectiveness of our notation…