Related papers: Simplicial arrangements on convex cones

We study a notion of convex cocompactness for discrete subgroups of the projective general linear group acting (not necessarily irreducibly) on real projective space, and give various characterizations. A convex cocompact group in this…

For a variety with a finitely generated total coordinate ring, we describe basic geometric properties in terms of certain combinatorial structures living in its divisor class group. For example, we describe the singularities, we calculate…

A Coxeter group admits infinite-dimensional irreducible complex representations if and only if it is not finite or affine. In this paper, we provide a construction of some of those representations for certain Coxeter groups using some…

Very recently Richter and Rogers proved that any convex geometry can be represented by a family of convex polygons in the plane. We shall generalize their construction and obtain a wide variety of convex shapes for representing convex…

In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…

Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on…

Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar…

Let $A$ be either a simplicial complex $K$ or a small category $\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \delta\colon…

We develop new techniques in the theory of convex surfaces to prove complete classification results for tight contact structures on lens spaces, solid tori, and T^2 X I. Erratum: In this note we seek to remedy errors which appeared in…

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…

The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of…

We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…

In this study, we delve into the discrete TC of surjective simplicial fibrations, aiming to unravel the interplay between topological complexity, discrete geometric structures, and computational efficiency. Moreover, we examine the…

We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…

We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that model categories satisfying a certain axiom are Quillen…

This paper aims to show that there exists a triangulation of the Heisenberg group $\mathbb{H}^n$ into singular simplexes with regularity properties on both the low-dimensional and high-dimensional layers. For low dimensions, we request our…

Convex or concave sequences of $n$ positive terms, viewed as vectors in $n$-space, constitute convex cones with $2n-2$ and $n$ extreme rays, respectively. Explicit description is given of vectors spanning these extreme rays, as well as of…

Let X be a space of constant curvature and P be a convex polyhedron in X. A Coxeter decomposition of the polyhedron P is a decomposition of P into finitely many Coxeter polyhedra, such that any two polyhedra having a common facet are…

In this article we prove two main results. Firstly, we show that any six-line arrangement, consisting of three pairs of mutually perpendicular lines, does not give rise to a "very generic or sufficiently general" discriminantal arrangement…