Related papers: Computing characteristic polynomials of hyperplane…

We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.

In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to…

In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.

We review results of papers written on the topic of polynomial amoebas with an emphasis on computational aspects of the topic. The polynomial amoebas have a lot of applications in various domains of science. Computation of the amoeba for a…

We give several families of polynomials which are related by Eulerian summation operators. They satisfy interesting combinatorial properties like being integer-valued at integral points. This involves nearby-symmetries and a recursion for…

Let $q$ be a positive integer. In our recent paper, we proved that the cardinality of the complement of an integral arrangement, after the modulo $q$ reduction, is a quasi-polynomial of $q$, which we call the characteristic…

This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. We first present two algorithms for the finite fields: one is based on Krylov iterates and Gaussian…

We introduce the package \textbf{arrangements} for the software CoCoA. This package provides a data structure and the necessary methods for working with hyperplane arrangements. In particular, the package implements methods to enumerate…

Determining the number of pieces after cutting a cake is a classical problem. Roberts (1887) provided an exact solution by computing the number of chambers contained in a plane cut by lines. About 88 years later, Zaslavsky (1975) even…

In~\cite{algorithmic} was given an algorithm that computes arithmetical structures on matrices. We use some of the ideas contained there to get an algorithm that computes arithmetical structures over dominated polynomials. A dominated…

We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation…

We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight…

We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…

We compute bifunctors cohomology for matrix polynomials under conjugation and detect candidates for universal classes in higher invariant theory.

We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…

An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…

We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer…