Related papers: On interrelations between strongly, weakly and cho…
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…
Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide…
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
An embedding of the complete bipartite graph $K_{3,3}$ in $\mathbb{P}^2$ gives rise to both a line arrangement and a bar-and-joint framework. For a generic placement of the six vertices, the graded Betti numbers of the logarithmic module of…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong…
We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras,…
We consider the restricted subsets of $\mathbb{N}_n=\{1,2,\ldots,n\}$ with $q\geq1$ being the largest member of the set $\mathcal{Q}$ of disallowed differences between subset elements. We obtain new results on various classes of problem…
We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda$ in such a way that each point of the space gets covered exactly $k$ times,…
We consider an algebraic treatment of a three-body system. In particular, we develop the formalism for a system of three identical objects and discuss an application to nonstrange baryon resonances which are interpreted as vibrational and…
We define novel fully combinatorial models of higher categories. Our definitions are based on a connection of higher categories to "directed spaces". Directed spaces are locally modelled on manifold diagrams, which are stratifications of…
Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…
Following an old result of Marcus and Schwarz we argue that in the heterotic string theory compactified on a seven dimensional torus, the target space duality group O(7,23;Z) and the strong-weak coupling duality transformations combine into…
Defant, Li, Propp, and Young recently resolved two enumerative conjectures of Propp concerning the tilings of regions in the hexagonal grid called benzels using two types of prototiles called stones and bones (with varying constraints on…
Several methods for studying the nature of a resonance are applied to resonances recently discovered in the bottonomium and charmonium sectors. We employ the effective-range expansion, the saturation of the width and compositeness of a…
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…
We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…
We describe a class of supersymmetric unified models with the following properties: i) the full breaking of the gauge group is achieved by Higgs fields in the fundamental representation; ii) the correct unification of the strong and…
A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs,…