Related papers: Spindle Starshaped Sets
The triangulations of point configurations which decompose as a free sum are classified in terms of the triangulations of the summands. The methods employ two new kinds of partially ordered sets to be associated with any triangulation of a…
This paper has partially a novel and partially a survey character. We start with a short review of rack (two term) homology of self distributive algebraic structures (shelves) and their connections to knot theory. We concentrate on a…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We classify an algebraic phenomenon on certain families of wreath products that can be seen as coming from a family of puzzles about switches on the corners of a spinning table. Such puzzles have been written about and generalized since…
The past decade has seen an increase of star formation studies made at the molecular cloud scale, motivated mostly by the deployment of a wealth of sensitive infrared telescopes and instruments. Embedded clusters, long recognised as the…
Stellar clusters are thought to be the simplest stellar systems and the closest observational counterparts to theoretical models for single stellar populations. Progress in our understanding of the atmospheres and evolution of massive stars…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be…
This paper explores the interplay between star operations, microscopic sets, and porous sets. The study focuses on the Galvin-Mycielski-Solovay theorem, which characterizes strongly measure zero sets and their interactions with meager sets.…
We prove that any compact semi-algebraic set is homeomorphic to the solution space of some art gallery problem. Previous works have established similar universality theorems, but holding only up to homotopy equivalence, rather than…
In this paper we study natural reconfiguration spaces associated to the problem of distributing a fixed number of resources to labeled nodes of a tree network, so that no node is left empty. These spaces turn out to be cubical complexes,…
We show that not every family of generalized microscopic sets forms an ideal. Moreover, we prove that some of these families have some weaker additivity properties and some of them do not have even that.
The analysis of the presence of substructures in 16 well-sampled clusters of galaxies suggests a stimulating hypothesis: Clusters could be classified as unimodal or bimodal, on the basis of to the sub-clump distribution in the {\em 3-D}…
In this paper, a selection of elegant, highly symmetric examples of three-periodic tangled nets and filaments are presented. They are constructed via familiar crystal nets using edges as geometric scaffolds for n-fold helical windings.…
In this paper, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental…
A Delone set in $\mathbb{R}^n$ is a set such that (a) the distance between any two of its points is uniformly bounded below by a strictly positive constant and such that (b) the distance from any point to the remaining points in the set is…
Spiral Galaxies is a pencil-and-paper puzzle played on a grid of unit squares: given a set of points called centers, the goal is to partition the grid into polyominoes such that each polyomino contains exactly one center and is 180{\deg}…
We study a special set of constellations of primes generated by twin primes.
While clusters of galaxies are considered one of the most important cosmological probes, the standard spherical modelling of the dark matter and the intracluster medium is only a rough approximation. Indeed, it is well established both…
We estimate the distribution of intrinsic shapes of the APM galaxy clusters from their corresponding distribution of projected shapes. We smooth the discrete galaxy distribution and define the cluster shape by fitting the best ellipse to…