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arXiv · 1305.2538

Cantor polynomials for semigroup sectors

Melvyn B. Nathanson
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Abstract

A packing function on a set Omega in R^n is a one-to-one correspondence between the set of lattice points in Omega and the set N_0 of nonnegative integers. It is proved that if r and s are relatively prime positive integers such that r divides s-1, then there exist two distinct quadratic packing polynomials on the sector {(x,y) \in \R^2 : 0 \leq y \leq rx/s}. For the rational numbers 1/s, these are the unique quadratic packing polynomials. Moreover, quadratic quasi-polynomial packing functions are constructed for all rational sectors.

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Melvyn B. Nathanson. 2013-05-11. Cantor polynomials for semigroup sectors. https://arxiv.org/abs/1305.2538

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