Related papers: Convex domino towers
We will use different way (in this work) from the existing methods in the literature which speaking in the separation of convex sets was carried out by hyperplanes. We are examining the behavior of convex set which is the domain of convex…
For an arbitrary smooth n-dimensional Fano variety $X$ we introduce the notion of a small toric degeneration. Using small toric degenerations of Fano n-folds $X$, we propose a general method for constructing mirrors of Calabi-Yau complete…
We construct a polygonal spiral by arranging a sequence of regular $n$-gons such that each $n$-gon shares a specified side and vertex with the $(n+1)$-gon in the construction. By offering flexibility for determining the size of each $n$-gon…
We apply column generation to approximating complex structured objects via a set of primitive structured objects under either the cross entropy or L2 loss. We use L1 regularization to encourage the use of few structured primitive objects.…
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…
The problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting (perfect) matchings of some subgraph of an Aztec diamond graph A_n, or more generally calculating the sum of the weights…
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric combinatorics such as tight spans of finite metric spaces…
This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor networks, we provide new and improved results on the matter using…
In this paper, constructions of regular pentagon and decagon, and the calculation of the main trigonometric ratios of the corresponding central angles are approached. In this way, for didactic purposes, it is intended to show the reader…
We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their graphs, f-vectors, and face lattices. The technique applies…
In this paper, we will give an overview of known and new techniques on how one can obtain explicit equations for candidates of good towers of function fields. The techniques are founded in modular theory (both the classical modular theory…
Motivated by particle phyiscs results, we investigate certain dyonic solutions in arbitrary dimensions. Concretely, we study the stringy constructions of such objects from concrete compactifications. Then we elaborate their tensor network…
Star-shaped bodies are an important nonconvex generalization of convex bodies (e.g., linear programming with violations). Here we present an efficient algorithm for sampling a given star-shaped body. The complexity of the algorithm grows…
We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential…
Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual…
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
We consider the efficient construction of polynomial lattice rules, which are special cases of so-called quasi-Monte Carlo (QMC) rules. These are of particular interest for the approximate computation of multivariate integrals where the…
We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable…
In this paper, we provide methods to automatically obtain automata that generate polyominoes inscribed in a rectangle of fixed width and increasing height. We use them to obtain the generating function of those sequences for small widths.
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…