Related papers: Equilateral sets in finite-dimensional normed spac…
In this article we find some sufficient conditions for the set in the Bilateral Grand Lebesgue Space to be compact set. We consider applications into numerical methods and in the basis problem.
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…
An MSTD set is a finite set of integers with more sums than differences. It is proved that, for infinitely many positive integers $k$, there are infinitely many affinely inequivalent MSTD sets of cardinality $k$. There are several related…
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
We consider extension of a closure system on a finite set S as a closure system on the same set S containing the given one as a sublattice. A closure system can be represented in different ways, e.g. by an implicational base or by the set…
In this paper, we report on the largest labelled dataset constructed so far for solving zero-dimensional square nonlinear systems with subdivision-based methods. A brief, non-exhaustive survey with emphasis on the literature from the past…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
Let $\mathcal{K}$ be a discrete valued field with finite residue field. In analogy with orthogonality in the Euclidean space $\mathbb{R}^n$, there is a well-studied notion of "ultrametric orthogonality" in $\mathcal{K}^n$. In this paper,…
We call a family $\{Y_1,\dots,Y_I\}$ in Euclidean space an equidistance spacing if $\|y_i - y_j\| = 1$ whenever $y_i \in Y_i, y_j \in Y_j$ and $i \neq j$. In other words, choosing a representative from each set produces a complete distance…
Motivated by constructions from applied topology, there has been recent interest in the homological algebra of linear representations of posets, particularly in the context of homological algebra relative to non-standard exact structures. A…
In this paper we continue the investigation of finding the max/min polygons which can be inscribed in a given triangle. Here we are concerned with equilateral triangles. This may seem uninteresting or benign at first, but there are some…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
For a certain class of finite posets, we prove that all their irreducible orthoscalar representations are finite-dimensional and describe those, for which there exist essential (non-degenerate) irreducible orthoscalar representations.
We give a geometric characterization of self-extremal sets in $L_p(\Om)$ spaces that partially extends our previous results to the case of $L_p$\ spaces.
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
We give a geometric characterization of extremal sets in ell_p spaces that generalizes our previous result for such sets in Hilbert spaces.
For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.
In this paper an idea of soft linear spaces and soft norm on soft linear spaces are given and some of their properties are studied. Soft vectors in soft linear spaces are introduced and their properties are studied. Completeness of soft…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…