arXiv subjects

Kåre Schou Gjaldbæk

Publications and source records attributed to Kåre Schou Gjaldbæk.

2 recordsLinked to original sources

arXiv2023

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 Pólya.

math.NT↗

arXiv2021

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

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 $\mathbb{R}^2$.

math.NT↗