Multiplicity of Hexagon Numbers

Abstract

Summary Imagine you have an unlimited supply of congruent equilateral triangles. Polygon numbers are the number of these triangles used to tile a convex polygon. For example, triangle numbers are square integers n 2, where the positive integer n is the side length of a tiled equilateral triangle. Hexagon numbers are the number of triangles used to tile a convex hexagon, and can be realized by removing corners from a tiled equilateral triangle. The number of ways (multiplicity up to congruence) that a given hexagon number can be constructed geometrically from such tiles is the subject of our paper.