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

We study quadratic polynomials giving bijections from the integer lattice points of sectors of ${\mathbb{R}}^2$ onto ${\mathbb{N}}_0$ , called packing polynomials. We determine all quadratic packing polynomials on rational sectors. This generalizes results of Stanton, Nathanson, and Fueter and P'olya.