Related papers: On the tensor Permutation Matrices
Particle systems admit a variety of tensor product structures (TPSs) depending on the complete system of commuting observables chosen for the analysis. Different notions of entanglement are associated with these different TPSs. Global…
An invertible matrix is called a Perron similarity if one of its columns and the corresponding row of its inverse are both nonnegative or both nonpositive. Such matrices are of relevance and import in the study of the nonnegative inverse…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
We study a sequence transformation pipeline that maps certain sequences with rational generating functions to permutation-based sequence families of combinatorial significance. Many of the number triangles we encounter can be related to…
The subject of this paper is a simulation to that in [1] but here we consider substitutions corresponding to transpositions instead of replacements.
Entringer numbers occur in the Andr\'e permutation combinatorial set-up under several forms. This leads to the construction of a matrix-analog refinement of the tangent (resp. secant) numbers. Furthermore, closed expressions for the…
We give a formula for the inverse matrix to an infinite matrix with possibly noncommutative entries, generalizing the Newton interpolation formula and the Taylor formula.
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible…
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
Fermion mass matrices generally rotate in generation space under scale changes, which can lead to fermions of different generations transmuting into one another. The effect is examined in detail and its cross-section calculated for $\gamma…
Forming the product of two geometric spaces is one of the most basic operations in geometry, but in the spectral-triple formulation of non-commutative geometry, the standard prescription for taking the product of two real spectral triples…
It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads.
It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…
In the paper the notion of truncating twisting function from a cubical set to a permutahedral set and the corresponding notion of twisted Cartesian product of these sets are introduced. The latter becomes a permutocubical set that models in…
Given n quaternions we investigate the extent of non-commutativity of their multiple products, commutators and exponential products.
We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.