Related papers: Partial transpose of permutation matrices

An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so…

In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. These…

We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements…

This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…

In this paper, we will derive the real roots of certain sets of matrices with real entries. We will also demonstrate that real orthogonal matrices can have real root or be involutory. Eventually, we will represent idempotent matrices in a…

Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to…

An economic technique for calculation of polarized bremsstrahlung process is proposed, assuming typical atomic momentum transfer $q\ll m$. The adopted approach is based on the natural reduction of the matrix element to the form…

Different ways to describe a permutation, as a sequence of integers, or a product of Coxeter generators, or a tree, give different choices to define a simple permutation. We recollect few of them, define new types of simple permutations,…

We study the representation theory of the uniform block permutation algebra in the context of the representation theory of factorizable inverse monoids. The uniform block permutation algebra is a subalgebra of the partition algebra and is…

We establish a Pythagorean theorem for the absolute values of the blocks of a partitioned matrix. This leads to a series of remarkable operator inequalities.

Conformal transformations are obtained by demanding that the form of the metric change by a conformal factor. Nevertheless, this transformation of the metric is not taken into account when a variation of the action is performed. The basic…

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…

Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…

We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…

In this paper transformations for matrix orthogonal polynomials in the real line are studied. The orthogonality is understood in a broad sense, and is given in terms of a nondegenerate continuous sesquilinear form, which in turn is…

The partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of quantum states. The transform contains partial transposition as a special case. The scaling transform corresponds to partial…

Transformers are a type of neural network that have demonstrated remarkable performance across various domains, particularly in natural language processing tasks. Motivated by this success, research on the theoretical understanding of…

The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…

A simple Markov process is considered involving a diffusion in one direction and a transport in a transverse direction. Quantitative mixing rate estimates are obtained with limited assumptions about the transport field, which might be…

We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as…