Related papers: Centrally symmetric configurations of integer matr…
We deal with the complete-intersection property of maximally differential ideals. Also, we connect the Gorenstein homology of derivations to the Gorenstein property of the base rings. These equipped with some applications.
Lie admissible algebra structures, called center-symmetric algebras, are defined. Main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of…
For any odd prime $p$ we consider representations of a group of order $p$ in the symplectic group $Sp(p-1,Z[1/n])$ of $(p-1)\times(p-1)$-matrices over the ring $Z[1/n]$, $0\neq n\in N$. We construct a relation between the conjugacy classes…
The simplest case of a ring topology is numerically investigated using the Terahertz modeling. Numerical simulations demonstrate high level degree of complete synchronization. Some security implications for the Terahertz communication and…
The problem of computing the index of a coincidence isometry of the hyper cubic lattice $\mathbb{Z}^{n}$ is considered. The normal form of a rational orthogonal matrix is analyzed in detail, and explicit formulas for the index of certain…
Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of…
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…
The symmetric inverse semigroup $I(X)$ on a set $X$ is the collection of all partial bijections between subsets of $X$ with composition as the algebraic operation. We study a minimal Hausdorff inverse semigroup topologies on $I(X)$. When…
We study the singularity probability of random integer matrices. Concretely, the probability that a random $n \times n$ matrix, with integer entries chosen uniformly from $\{-m,\ldots,m\}$, is singular. This problem has been well studied in…
Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that…
We investigate the computational complexity of problems on toric ideals such as normal forms, Gr\"obner bases, and Graver bases. We show that all these problems are strongly NP-hard in the general case. Nonetheless, we can derive efficient…
In this article we present two new algorithms to compute the Groebner basis of an ideal that is invariant under certain permutations of the ring variables and which are both implemented in SINGULAR (cf. [DGPS12]). The first and major…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
In this paper we extend the idea of integration to generic algebras. In particular we concentrate over a class of algebras, that we will call self-conjugated, having the property of possessing equivalent right and left multiplication…
We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the location of the specified entries, and not their values, if…
Centraliser algebras of monomial representations of finite groups may be constructed and studied using methods similar to those employed in the study of permutation groups. Guided by results of D. G. Higman and others, we give an explicit…
Exact evaluation of $<{\rm Tr} S^p>$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary…
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…