Related papers: Minimal Constructible Sets

For any irrational cut-and-project setup, we demonstrate a natural infinite family of windows which gives rise to separated nets that are each bounded distance to a lattice. Our proof provides a new construction, using a sufficient…

A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

The set $S(n)$ of all elementary symmetric polynomials in $n$ variables is a minimal generating set for the algebra of symmetric polynomials in $n$ variables, but over a finite field ${\mathbb F}_q$ the set $S(n)$ is not a minimal…

The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…

We studied the construction problem of the unextendible product basis (UPB). We mainly give a method to construct a UPB of a quantum system through the UPBs of its subsystem. Using this method and the UPBs which are known for us, we…

This paper is a continuation of our previous works where we study maps from $X_0(N)$, $N \ge 1$, into $\mathbb P^2$ constructed via modular forms of the same weight and criteria that such a map is birational (see [12]). In the present paper…

This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising…

A classical theorem of Forster asserts that a finite module $M$ of rank $\leq n$ over a Noetherian ring of Krull dimension $d$ can be generated by $n + d$ elements. We prove a generalization of this result, with "module" replaced by…

We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like…

We consider a series of groups defined by Kim and Manturov. These groups have their background in triangulations of a surface and configurations of points, lines or circles on the surface. They are expected to have relationships to many…

Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.

We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…

Let $G$ be a nonabelian group. We say that $G$ has an abelian partition, if there exists a partition of $G$ into commuting subsets $A_1, A_2, \ldots, A_n$ of $G$, such that $|A_i|\geqslant 2$ for each $i=1, 2, \ldots, n$. This paper…

For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system's semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the…

We propose a procedure of constructing new block designs starting from a given one by looking at the intersections of its blocks with various sets and grouping those sets according to the structure of the intersections. We introduce a…

The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…

Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…

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…

We prove that any definable family of subsets of a definable infinite set $A$ in an o-minimal structure has cardinality at most $|A|$. We derive some consequences in terms of counting definable types and existence of definable topological…