Related papers: Additive Combinatorics in Groups and Geometric Com…
We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to…
We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a…
We introduce two families of inequalities. Large ensemble decoupling is connected to the continuous restriction phenomenon. Tight decoupling is connected to the discrete Restriction conjecture for the sphere. Our investigation opens new…
There are many papers studying properties of point sets in the Euclidean space $\mathbb{E}^m$ or on integer grids $\mathbb{Z}^m$, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the…
Let F be the field of two elements and G a finite abelian 2-group with an involutory automorphism. The extension of this automorphism to the group algebra FG is called an involutory involution. This determines the groups of unitary and…
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…
Given a finite set of points in general position in the plane or sphere, we count the number of ways to separate those points using two types of circles: circles through three of the points, and circles through none of the points (up to an…
We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups.
Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
The purpose of this paper is twofold. Firstly, we generalize the notion of characteristic polynomials of hyperplane and toric arrangements to those of certain abelian Lie group arrangements. Secondly, we give two interpretations for the…
We prove by using simple number-theoretic arguments formulae concerning the number of elements of a fixed order and the number of cyclic subgroups of a direct product of several finite cyclic groups. We point out that certain multiplicative…
We show, under some natural conditions, that the set of abelian (and thus also cyclotomic) multiplicatively dependent points on an irreducible curve over a number field is a finite union of preimages of roots of unity by a certain finite…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
Collection of (equivariant) $\rm{PL}$-mappings admitting a relative abelian, cyclic, quaternionic, bicyclic, and quaternionic-cyclic structures are constructed.