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arXiv · 2102.03392

Non-injectivity of Nonzero Discriminant Polynomials and Applications to Packing Polynomials

Kåre Schou Gjaldbæk
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Abstract

We show that an integer-valued quadratic polynomial on $\mathbb{R}^2$ can not be injective on the integer lattice points of any affine convex cone if its discriminant is nonzero. A consequence is the non-existence of quadratic packing polynomials on irrational sectors of $\mathbb{R}^2$.

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Kåre Schou Gjaldbæk. 2021-02-05. Non-injectivity of Nonzero Discriminant Polynomials and Applications to Packing Polynomials. https://arxiv.org/abs/2102.03392

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