Related papers: Local generation of tilings
We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As…
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…
We consider groups of the form $G=AB$ with two locally cyclic subgroups $A$ and $B$. The structure of these groups is determined in the cases when $A$ and $B$ are both periodic or when one of them is periodic and the other is not. Together…
This is the sequel paper to arXiv:2108.07185, continuing a study of monogenicity of number rings from a moduli-theoretic perspective. By the results of the first paper in this series, a choice of a generator $\theta$ for an $A$-algebra $B$…
In this paper, a method to generate permutations of a string under a set of constraints decided by the user is presented. The required permutations are generated without generating all the permutations.
Context and motivation: Software Product Lines (SPL) enable the creation of software product families with shared core components using feature models to model variability. Choosing features from a feature model to generate a product may…
A continuum description of unstructured meshes in two dimensions, both for planar and curved surface domains, is proposed. The meshes described are those which, in the limit of an increasingly finer mesh (smaller cells), and away from…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that…
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…
We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between $\infty$-tilting objects in complete, cocomplete abelian categories with an…
Motivated by applications in reliable and secure communication, we address the problem of tiling (or partitioning) a finite constellation in $\mathbb{Z}_{2^L}^n$ by subsets, in the case that the constellation does not possess an abelian…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
We study the `local entanglement' remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of…
Our earlier article proved that if $n > 1$ translates of sublattices of $Z^d$ tile $Z^d$, and all the sublattices are Cartesian products of arithmetic progressions, then two of the tiles must be translates of each other. We re-prove this…
The importance of neighborhood construction in local explanation methods has been already highlighted in the literature. And several attempts have been made to improve neighborhood quality for high-dimensional data, for example, texts, by…
We study the density of periodic configurations for shift spaces defined on (the Cayley graph of) a finitely generated group. We prove that in the case of a full shift on a residually finite group and in that of a group shift space on an…
A problem of constructing of local definitions for formations of finite groups is discussed in the article. The author analyzes relations between local definitions of various types. A new proof of existence of an $\omega$-composition…
We discuss to what extent the local techniques of resolution of singularities over fields of characteristic zero can be applied to improve singularities in general. For certain interesting classes of singularities, this leads to an embedded…
Self-similar space-filling bearings have been proposed some time ago as models for the motion of tectonic plates and appearance of seismic gaps. These models have two features which, however, seem unrealistic, namely, high symmetry in the…