Related papers: On the determinant of multiplication map of a mono…

We study the Macaulay coefficients induced by the ideal and quotient segments of a degree-$\delta$ monomial in $n$ variables. We give explicit formulas for these coefficients and establish a duality between the two theories. Our main result…

Let $K:={x: g(x)\leq 1}$ be the compact sub-level set of some homogeneous polynomial $g$. Assume that the only knowledge about $K$ is the degree of $g$ as well as the moments of the Lebesgue measure on $K$ up to order 2d. Then the vector of…

Let $X_{2k}$ be a set of $2k$ labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of $X_{2k}$. Two such matchings, $M$ and $M'$, are disjoint compatible if they do not have…

We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column-(row-)determinants, often used…

We consider a large family of dynamical Belyi maps of arbitrary degree and study the arithmetic monodromy groups attached to the iterates of such maps. Building on the results of Bouw-Ejder-Karemaker on the geometric monodromy groups of…

We discuss tangent maps related to the multipliers of periodic points of a typical one-dimensional polynomial map.

We consider polynomial maps described by so-called "(multivariate) linearized polynomials". These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps…

Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…

We determine sets of elements which, under certain conditions, generate an intersection of ideals up to radical.

Given an admissible map F for a homogeneous network N, it is known that the Jacobian DF(x) around a fully synchronous point x = (x0, ..., x0) is again an admissible map for N. Motivated by this, we study the spectra of linear admissible…

We show how the matrix algebra notions of determinant, spectrum, and Hermitian conjugation transfer to the Clifford algebra and to differential forms on parallelisable manifolds.

In this article we give explicit descriptions of the multiplicities of some classes of monomial ideals. For instance, we give a formula for the multiplicities of all codimension 1 monomial ideals, and another formula for the multiplicities…

We interpret the combinatorial Mandelbrot set in terms of \it{quadratic laminations} (equivalence relations $\sim$ on the unit circle invariant under $\sigma_2$). To each lamination we associate a particular {\em geolamination} (the…

It is well known that a monomial complete intersection has the strong Lefschetz property in characteristic zero. This property is equivalent to the statement that any power of the sum of the variables is a maximal rank element on the…

The derivation of zonal polynomials involves evaluating the integral \[ \exp\left( - \frac{1}{2} \operatorname{tr} D_{\beta} Q D_{l} Q \right) \] with respect to orthogonal matrices \(Q\), where \(D_{\beta}\) and \(D_{l}\) are diagonal…

In this work it is shown that the SD-KE decomposition is multiplicative under determinantal-type functions for graphs with perfect matchings, providing a new tool for the study of unimodular and singular matchable graphs.

We present an algorithm which for any given ideal $I\subseteq\mathbb{K} [x,y]$ finds all elements of $I$ that have the form $f(x) - g(y)$, i.e., all elements in which no monomial is a multiple of $xy$.

The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…

A result of I.V.Dolgachev states that the complex homaloidal polynomials in three variables, i.e. the complex homogeneous polynomials whose polar map is birational, are of degree at most three. In this note we describe homaloidal…

Let $S = K[x_1, \ldots, x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $\mathrm{deg}\ x_i = 1$ and $I \subset S$ a homogeneous ideal of $S$ with $\dim S/I = d$. The Hilbert series of $S/I$ is of the form…