Related papers: Characteristic elements for real hyperplane arrang…

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 first give a combinatorial interpretation of coefficients of Chebyshev polynomials, which allows us to connect them with compositions of natural numbers. Then we describe a relationship between the number of compositions of a natural…

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of…

Characteristic quasi-polynomials enumerate the number of points in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic quasi-polynomials of the restrictions of the Shi…

We consider a family of generic weighted arrangements of $n$ hyperplanes in $\C^k$ and show that the Gauss-Manin connection for the associated hypergeometric integrals, the contravariant form on the space of singular vectors, and the…

In this paper we characterize the effect algebras whose sharp and principal elements coincide. We also give examples of two non-isomorphic effect algebras having the same universum, partial order and orthosupplementation.

We describe the T-space of central polynomials for both the unitary and the nonunitary finite dimensional Grassmann algebra over a field of characteristic p not equal to 2 (infinite field in the case of the unitary algebra).

In this article we shows some results about algebra with the group of units having special polynomial identity.

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary…

We introduce the notion of semi-characteristic polynomial for a semi-linear map of a finite- dimensional vector space over a field of characteristic p. This polynomial has some properties in common with the classical characteristic…

A central question in the study of line arrangements in the complex projective plane $\mathbb{CP}^2$ is: when does the combinatorial data of the arrangement determine its topological properties? In the present work, we introduce a…

Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…

We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of type $A_n$, $B_n$, and $D_n$, the coefficients of the characteristic polynomial of the reflection…

It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…

We study some properties and perspectives of the Hurwitz series ring $H_R[[t]]$, for a commutative ring with identity $R$. Specifically, we provide a closed form for the invertible elements by means of the complete ordinary Bell…

We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex…

With a main tool is signed graphs, we give a full description of the characteristic quasi-polynomials of ideals of classical root systems ($ABCD$) with respect to the integer and root lattices. As a result, we obtain a full description of…

Let $\mathcal{A}$ be an affine hyperplane arrangement, $L(\mathcal{A})$ its intersection poset, and $\chi_{\mathcal{A}}(t)$ its characteristic polynomial. This paper aims to propose combinatorial structures for the factorization of…

We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…

In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real $(\beta = 1)$, complex ($\beta = 2)$ and real…