The surface of a lattice polytope
G\'abor Heged\"us
TL;DR
This paper presents simple formulas for calculating the surface area of d-dimensional lattice polytopes by applying Ehrhart theory, providing a new approach to understanding their geometric properties.
Contribution
It introduces novel formulas for the surface area of lattice polytopes based on Ehrhart theory, simplifying previous methods.
Findings
Derived explicit formulas for surface area using Ehrhart polynomials
Extended Ehrhart theory applications to geometric surface measurements
Provided a new computational approach for lattice polytope analysis
Abstract
My main results are simple formulas for the surface area of d-dimensional lattice polytopes using Ehrhart theory.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic Geometry and Number Theory · Point processes and geometric inequalities