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

Madeline Brandt; Kåre Schou Gjaldbæk

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arXiv · 2102.13578

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

Madeline Brandt·Kåre Schou Gjaldbæk

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Abstract

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.

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Madeline Brandt, Kåre Schou Gjaldbæk. 2021-02-26. Classification of Quadratic Packing Polynomials on Sectors of $\mathbb{R}^2$. https://arxiv.org/abs/2102.13578

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