Related papers: A combinatorial characterisation of embedded polar…
In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…
Our study explores the mixture of polar particles in apolar environment. We employ a coarse-grained approach to model the mixture, where polar particles are in minority. The interaction between polar and apolar components is incorporated…
This paper is a combinatorial and computational study of the moduli space of tropical curves of genus g, the moduli space of principally polarized tropical abelian varieties, and the tropical Torelli map. These objects were introduced…
For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…
Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our approach is based on…
Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular…
A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…
A conduction electron (or hole) together with its self-induced polarisation in a polar semiconductor or an ionic crystal forms a quasi-particle, which is called a polaron. The polaron concept is of interest, not only because it describes…
Let $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For a subset $A\subseteq G$, we put $\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is…
The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor…
We investigate how coarse embeddability of box spaces into Hilbert space behaves under group extensions. In particular, we prove a result which implies that a semidirect product of a finitely generated free group by a finitely generated…
We review our current knowledge about a particular case of decoupled gas kinematics -- inner ionized-gas polar disks. Though more difficult to be noticed, they seem to be more numerous than their large-scale counterparts; our recent…
The notion of a Heffter array, which received much attention in the last decade, is equivalent to a pair of orthogonal Heffter systems. In this paper we study the existence problem of a set of $r$ mutually orthogonal Heffter systems for any…
We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results…
We show that if a topological or paratopological group $G$ contains a stationary subset of some regular uncountable cardinal, then $G$ contains a subspace which is not collectionwise normal. This statement implies that if a monotonically…
We study representations of tropical linear spaces as intersections of tropical hyperplanes of circuits. For several classes of matroids, we describe minimal tropical bases. We also show that every realizable tropical linear space has a…
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective…
We study certain physically-relevant subgeometries of binary symplectic polar spaces $W(2N-1,2)$ of small rank $N$, when the points of these spaces canonically encode $N$-qubit observables. Key characteristics of a subspace of such a space…