Cantor Polynomials and the Fueter-Pólya Theorem. Issue 10 (1st December 2016)

• Record Type: Journal Article
• Authors: Nathanson, Melvyn B.
• Is Part Of: American Mathematical Monthly. Volume 123:Issue 10(2016)
• Page Start: 1001
• Page End: 1012
• Publication Date: 2016-12-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/amer.math.monthly.123.10.1001
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: A packing polynomial is a polynomial that maps the set N 2 0 of lattice points with nonnegative coordinates bijectively onto N0 . Cantor constructed two quadratic packing polynomials, and Fueter and Pólya proved analytically that the Cantor polynomials are the only quadratic packing polynomials. The purpose of this paper is to present a beautiful elementary proof of Vsemirnov of the Fueter–Pólya theorem. It is a century-old conjecture that the Cantor polynomials are the only packing polynomials on N 2 0 .