Related papers: On Dendrites Generated By Symmetric Polygonal Syst…

We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…

The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between…

If two homogeneous IFSs satisfying the OSC with opposite common contraction factors share the same attractor on the real line, we show that this attractor is symmetric. This answers a question of Feng and Wang [Adv. Math. 222 (2009),…

We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other…

We study cyclic sieving phenomena (CSP) on combinatorial objects from an abstract point of view by considering a rational polyhedral cone determined by the linear equations that define such phenomena. Each lattice point in the cone…

In this paper, we focus on a special class of symmetric tensors, which can be orthogonally diagonalizable, and investigate their Z-eigenpairs problem. We show that the eigenpairs can be uniformly expressed using several basic eigenpairs,…

We study conditions on polynomials such that the ideal generated by their orbits under the symmetric group action becomes a monomial ideal or has a monomial radical. If the polynomials are homogeneous, we expect that such an ideal has a…

Let G be a simple complex algebraic group. We prove that the irregularity of the adjoint connection of an irregular flat G-bundle on the formal punctured disk is always greater than or equal to the rank of G. This can be considered as a…

The independence complex of a graph G is a simplicial complex whose simplices are the independent sets in G. In the last couple of decades, the independence complexes of square grids (with various boundary conditions) have gained much…

Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In the present paper we highlight their connections to the Kuramoto synchronization model in physics -- where they are called adjacency…

Cycloids, hipocycloids and epicycloids have an often forgotten common property: they are homothetic to their evolutes. But what if use convex symmetric polygons as unit balls, can we define evolutes and cycloids which are genuinely…

The homogeneous coordinate ring of a Schubert variety (a Schubert cycle for short) is an algebra with straightening law generated by a distributive lattice. This paper gives a simple method to study the set of all the join-irreducible…

In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the…

Let $P=A_1\ldots A_n$ be a generic polygon in three-dimensional space and let $v_1,v_2,\ldots,v_n$ be vectors $\overline{A_1A_2},\overline{A_2A_3},\ldots,\overline{A_nA_1}$, respectively. $P$ will be called \emph{regular}, if there exist…

On the generalized tangent bundle of a smooth manifold, we study skew-symmetric endomorphism satisfying an arbitrary polynomial equation with real constant coefficients. We study the compatibility of these structures with the de Rham…

The aim of this paper is to show that the existence of attracting sets for quasiperiodically forced systems can be extended to appropriate skew-products on the cylinder, homotopic to the identity, in such a way that the general system will…

The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be…

Generalizing the octahedral configuration of six congruent cylinders touching the unit sphere, we exhibit configurations of congruent cylinders associated to a pair of dual Platonic bodies.

Motivated by the graph associahedron KG, a polytope whose face poset is based on connected subgraphs of G, we consider the notion of associativity and tubes on posets. This leads to a new family of simple convex polytopes obtained by…

We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytopes theory, we introduce the concept of chirality, a…