Packing Polynomials and the Fueter-Polya Theorem

Speaker: Chaitanya Tappu 

Date: 6th February 2018 (Tuesday)
Time: 09:15 pm-10:15 pm
Venue: Lecture Hall I, Department of Mathematics
 
Abstract: A polynomial of two (real) variables that maps \mathbb N \times \mathbb N bijectively onto \mathbb N is called a packing polynomial. Cantor’s diagonal enumeration provides us with one packing polynomial, and is used to prove that rationals are countably infinite. Packing polynomials find other uses too—to store two-(multi-)dimensional arrays in linear memory. The Fueter-Polya theorem (1923) asserts that there are just two quadratic packing polynomials—Cantor’s polynomial and its reflection. In this talk I’ll present an elementary proof of this theorem due to M.A. Vsemirnov (2001).
Pre-requisites: School algebra. Knowledge of congruences/modular arithmetic would help, but can be covered in the talk if necessary.
Area: Computer Science, Number Theory
References:
  1. Lew, J. S. (1981). Polynomials in two variables taking distinct integer values at lattice-points. The American Mathematical Monthly, 88(5):344–346.
  2. Nathanson, M. B. (2016). Cantor polynomials and the Fueter-Polya theorem. The American Mathematical Monthly, 123(10):1001–1012. https://arxiv.org/abs/1512.08261.

 

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