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

Source: [Non-injectivity of Nonzero Discriminant Polynomials and Applications to Packing Polynomials](<https://www.sota2.com/research/paper/68fa57c81e209131ce9a84d6>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T14:55:35.481Z

Authors: K{\\aa}re Schou Gjaldb{\\ae}k

Published: 2021-02-05T19:34:14.000Z

## 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 $\\mathbb{R}^2$.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2102.03392>)

[PDF](<https://arxiv.org/pdf/2102.03392.pdf>)