CANTOR POLYNOMIALS FOR SEMIGROUP SECTORS

Abstract

A packing function on a set Ω in Rn is a one-to-one correspondence between the set of lattice points in Ω and the set N0 of non-negative 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) ∈ R2 : 0 ≤ y ≤ 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.