Related papers: Higher genus universally decodable matrices (UDMG)
In this paper we introduce a new parameter for a graph called the {\it minimum universal rank}. This parameter is similar to the minimum rank of a graph. For a graph $G$ the minimum universal rank of $G$ is the minimum rank over all…
A curve of genus g is maximal Mumford (MM) if it has g+1 ovals and g tropical cycles. We construct full-dimensional families of MM curves in the Hilbert scheme of canonical curves. This rests on first-order deformations of graph curves…
Column closed pattern subgroups $U$ of the finite upper unitriangular groups $U_n(q)$ are defined as sets of matrices in $U_n(q)$ having zeros in a prescribed set of columns besides the diagonal ones. We explain Jedlitschky's construction…
A matrix $M$ over the finite field $ \mathbb{F}_q $ is called \emph{maximum distance separable} (MDS) if all of its square submatrices are non-singular. These MDS matrices are very important in cryptography and coding theory because they…
Let $M$ be an arbitrary matroid with circuits $\mathcal{C}(M)$. We propose a definition of a derived matroid $\delta M$ that has as its ground set $\mathcal{C}(M)$. Unlike previous attempts of such a definition, our definition applies to…
We consider the group M of all polynomial matrices U(z) = U0 + U1*z + U2*z*z +...+Uk*z*...*z, k=0,1,... that satisfy equation U(z)*D*U(z)" = D with the diagonal n*n matrix D=diag{-1,1,1,...1}. Here n > 1, U(z)" = U0" + U1"*z + U2"*z*z +…
Let $F$ be an infinite field and $UT(d_1,\dots, d_n)$ be the algebra of upper block-triangular matrices over $F$. In this paper we describe a basis for the $G$-graded polynomial identities of $UT(d_1,\dots, d_n)$, with an elementary grading…
A Mumford group is a discontinuous subgroup $\Gamma$ of PGL(2,K), where K denotes a non archimedean valued field, such that the quotient by $\Gamma$ is a curve of genus 0. As abstract group $\Gamma$ is an amalgam of a finite tree of finite…
In this paper, we study the irreducibility of $\mathcal{U}(\mathfrak{g})^{G'}$-modules on the spaces of intertwining operators in the branching problem of reductive Lie algebras, and construct a family of finite-dimensional irreducible…
Let G be a simple, simply connected algebraic group defined over an algebraically closed field k of positive characteristic p. Let \sigma:G->G be a strict endomorphism (i. e., the subgroup G(\sigma) of \sigma-fixed points is finite). Also,…
In this paper, we analyze $m$-dimensional ($m$D) convolutional codes with finite support, viewed as a natural generalization of one-dimensional (1D) convolutional codes to higher dimensions. An $m$D convolutional code with finite support…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
We detail the automatic construction of R matrices corresponding to (the tensor products of) the (0|\alpha) families of highest-weight representations of the quantum superalgebras U_q[gl(m|n)]. These representations are irreducible, contain…
A dimension group is a partially ordered countable group such that (1) every finite subset is contained in an ordered subgroup which is a finite direct power of Z and (2) the group has an order unit i.e. a positive element u such that every…
We give a general lower bound on the rank of matrices of the form $\rho(h) - I$ with $\rho : G \rightarrow GL({\mathbb F}^n)$ an irreducible representation of a finite group $G$. The main tool in the proof is a (strengthening) of a…
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
Following a review of related results in rigidity theory, we provide a construction to obtain generically universally rigid frameworks with the minimum number of edges, for any given set of n nodes in two or three dimensions. When a set of…
The universal adjacency matrix $U$ of a graph $\Gamma$, with adjacency matrix $A$, is a linear combination of $A$, the diagonal matrix $D$ of vertex degrees, the identity matrix $I$, and the all-1 matrix $J$ with real coefficients, that is,…
While dealing with the nontrivial task of classifying Mueller matrices, of special interest is the study of the degenerate Mueller matrices (matrices with vanishing determinant, for which the law of multiplication holds, but there exists no…
We construct explicit dominant, rational morphisms from projective bundles over rational varieties to relevant moduli spaces, showing their unirationality. These constructions work for $U_{r,d,g}$; for all ranks, degrees and genus $2\leq g…