Related papers: Multidimensional permanents of polystochastic matr…

Any discrete distribution with support on $\{0,\ldots, d\}$ can be constructed as the distribution of sums of Bernoulli variables. We prove that the class of $d$-dimensional Bernoulli variables $\boldsymbol{X}=(X_1,\ldots, X_d)$ whose sums…

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…

We give an explicit construction, based on Hadamard matrices, for an infinite series of floor{sqrt{d}/2}-neighborly centrally symmetric d-dimensional polytopes with 4d vertices. This appears to be the best explicit version yet of a recent…

We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a $2$-dimensional subspace forms a Hadamard matrix. It is shown that such a matrix of order $n$ exists, if…

The free closed semialgebraic set $D_f$ determined by a hermitian noncommutative polynomial $f$ is the closure of the connected component of $\{(X,X^*)\mid f(X,X^*)>0\}$ containing the origin. When $L$ is a hermitian monic linear pencil,…

We consider the set of points chosen randomly, independently and uniformly in the $d$-dimensional spherical layer. A set of points is called $1$-convex if all its points are vertices of the convex hull of this set. In \cite{3} an estimate…

Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…

Generalized permutahedra are the polytopes obtained from the permutahedron by changing the edge lengths while preserving the edge directions, possibly identifying vertices along the way. We introduce a "lifting" construction for these…

A bistochastic matrix is a square matrix with positive entries such that rows and columns sum to unity. A unistochastic matrix is a bistochastic matrix whose matrix elements are the absolute values squared of a unitary matrix. We can now…

We characterize the edges of two classes of $0/1$-polytopes. The first class corresponds to the stable set polytope of a graph $G$ and includes chain polytopes of posets, some instances of matroid independence polytopes, as well as…

An $n \times n$ matrix with $\pm 1$ entries which acts on $\mathbb{R}^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices…

Permutons, which are probability measures on the unit square $[0, 1]^2$ with uniform marginals, are the natural scaling limits for sequences of (random) permutations. We introduce a $d$-dimensional generalization of these measures for all…

Be d_{m,n} a generic element in the infinite matrix D, with d_{1, n} defined as the n-th prime number and, for any m>1, d_{m, n} = | d_{m-1, n} - d_{m-1, n+1} | When n>1, after the first few terms the columns in the matrix appear to be…

We prove that the following statements are equivalent: a linear matrix equation with parameters forming a commuting set of diagonalizable matrices is consistent, a certain matrix constructed with the Drazin inverse is a solution of this…

In this paper we give a matrix version of Handelman's Positivstellensatz [1], representing polynomial matrices which are positive definite on convex, compact polyhedra. Moreover, we propose also a procedure to find such a representation. As…

An \emph{interval vector} is a $(0,1)$-vector in $\mathbb{R}^n$ for which all the 1's appear consecutively, and an \emph{interval-vector polytope} is the convex hull of a set of interval vectors in $\mathbb{R}^n$. We study three particular…

The rank of an n x n matrix A is equal to the size of its largest square submatrix with a nonzero determinant, and it can be computed in O(n^2.37) time. Analogously, the size of the largest square submatrix with nonzero permanent is defined…

The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…

Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $\theta^{\mu\nu}(\tau)$ instead of the numerical matrix. The corresponding Poincare…

The crumpled-to-flat phase transition that occurs in D-dimensional polymerized phantom membranes embedded in a d-dimensional space is investigated nonperturbatively using a field expansion up to order eight in powers of the order parameter.…