Integral points in rational polygons: a numerical semigroup approach

On Counting Integral Points in a Convex Rational Polytope

Given a convex rational polytope b = x ∈ n+ Ax= b , we consider the function b → f b , which counts the nonnegative integral points of b . A closed form expression of its -transform z → z is easily obtained so that f b can be computed as the inverse -transform of . We then provide two variants of an inversion algorithm. As a by-product, one of the algorithms provides the Ehrhart polynomial of a...

Distribution of Rational Points: A Survey

Rational Angled Hyperbolic Polygons

We prove that every rational angled hyperbolic triangle has transcendental side lengths and that every rational angled hyperbolic quadrilateral has at least one transcendental side length. Thus, there does not exist a rational angled hyperbolic triangle or quadrilateral with algebraic side lengths. We conjecture that there does not exist a rational angled hyperbolic polygon with algebraic side ...

A Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

Addition Behavior of a Numerical Semigroup 23

— In this work we study some objects describing the addition behavior of a numerical semigroup and we prove that they uniquely determine the numerical semigroup. We then study the case of Arf numerical semigroups and find some specific results. Résumé (Comportement de l’addition dans un semi-groupe numérique). — Dans ce travail, nous étudions des objets qui décrivent le comportement de l’additi...