Related papers: Equations and multidegrees for inverse symmetric m…

Consider the $n$th degree polynomial equation, $X^n+A_{n-1}X^{n-1}+...+A_1X+A_0=0$ over the ring of 2 by 2 complex matrices. If this equation has more than ${2n \choose 2}$ solutions, then it has infinitely many solutions. We show here that…

The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal…

We give an explicit formula for the duality, previously conjectured by Horja and Borisov, of two systems of GKZ hypergeometric PDEs. We prove that in the appropriate limit this duality can be identified with the inverse of the Euler…

In this paper we study the equations of the elimination ideal associated with $n+1$ generic multihomogeneous polynomials defined over a product of projective spaces of dimension $n$. We first prove a duality property and then make this…

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the…

In this work, we explicitly compute the group inverse of symmetric and periodic Jacobi matrices.

We prove several new sufficient conditions for hamiltonicity and bipancyclicity in balanced bipartite digraphs, in terms of sums of degrees over dominating or dominated pairs of vertices.

We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…

We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over…

This paper contains the proof of difference counterparts of the conjectures due to Keven Kadell on symmetric and anti-symmetric Macdonald polynomials.

We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.

We extend Krivine's strict positivstellensatz for usual (real multivariate) polynomials to symmetric matrix polynomials with scalar constraints. The proof is an elementary computation with Schur complements. Analogous extensions of Schm\"…

We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…

This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to…

We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory we give a proof of a result of Helmke, Jordan and Lieb on the number of linear unimodular matrix polynomials over a finite…

In this letter we study a class of symmetries of the new translational extended shape invariant potentials. It is proved that a generalization of a compatibility condition introduced in a previous article is equivalent to the usual shape…

We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…

We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and…