Quadratic Packing Polynomials on Sectors of ${\mathbb{R}}^2$

Abstract

A polynomial $p(x,y)$ on a region $S$ in the plane is called a packing polynomial if the restriction of $p(x,y)$ to $S\cap {\mathbb{Z}}^2$ yields a bijection to $\mathbb{N}$. In this paper, we determine all quadratic packing polynomials on rational sectors of ${\mathbb{R}}^2$.

14 pages, 2 figures