Related papers: Convex domino towers
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We give a new combinatorial proof for the number of convex polyominoes whose minimum enclosing rectangle has given dimensions. We also count the subclass of these polyominoes that contain the lower left corner of the enclosing rectangle…
Given a web (multi-foliation) and a linear system on a projective surface we construct divisors cutting out the locus where some element of the linear system has abnormal contact with the leaf of the web. We apply these ideas to reobtain a…
We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict…
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
In this study, the properties of convex hexagons that can form rotationally symmetric edge-to-edge tilings are discussed. Because the convex hexagons are equilateral convex parallelohexagons, convex pentagons generated by bisecting the…
Exact solutions construction in scalar fields cosmology is of growing interest. In this work we review the results which obtained with the help of one of the most effective method. Namely, the method of generating functions for exact…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
Domain wall - type solution with oscillating thickness in a real, scalar field model is investigated with the help of a polynomial approximation. We propose a simple extension of the polynomial approximation method. In this approach we…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
Elkies proposed a procedure for constructing explicit towers of curves, and gave two towers of Shimura curves as relevant examples. In this paper, we present a new explicit tower of Shimura curves constructed by using this procedure.
In this paper, we propose DDPM-Polycube, a generative polycube creation approach based on denoising diffusion probabilistic models (DDPM) for generating high-quality hexahedral (hex) meshes and constructing volumetric splines. Unlike…
This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function…
We present an algorithm to find generators of the multigraded algebra A associated to an arbitrary p-divisor D on some variety Y. A modified algorithm is also presented for the case where Y admits a torus action. We demonstrate our…
There are known constructions for some regular polygons, usually inscribed in a circle, but not for all polygons - the Gauss-Wantzel Theorem states precisely which ones can be constructed. The constructions differ greatly from one polygon…
A well-known result in the study of convex polyhedra, due to Minkowski, is that a convex polyhedron is uniquely determined (up to translation) by the directions and areas of its faces. The theorem guarantees existence of the polyhedron…
We establish a general method for generating reflections between categories. We then apply our technique to generate adjunctions starting from geometric morphisms between Grothendieck toposes; as particular cases, we recover various…
Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local…
We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…
We survey techniques for constructing spaces with non-trivial self covers. These processes include methods for building low and high dimension continua which non-trivially self. We also discuss several related group theoretic and…