Journal of Combinatorics

Volume 7 (2016)

Number 1

The Prouhet–Tarry–Escott problem and generalized Thue–Morse sequences

Pages: 117 – 133

DOI: https://dx.doi.org/10.4310/JOC.2016.v7.n1.a5

Authors

Ethan D. Bolker (Department of Computer Science and Department of Mathematics, University of Massachusetts, Boston, Mass., U.S.A.)

Carl Offner (Department of Computer Science, University of Massachusetts, Boston, Mass., U.S.A.)

Robert Richman (Department of Chemistry and Biochemistry, University of Maryland, College Park, Md., U.S.A.)

Catalin Zara (Department of Mathematics, University of Massachusetts, Boston, Mass., U.S.A.)

Abstract

We present new methods of generating Prouhet–Tarry–Escott partitions of arbitrarily large regularity. One of these methods generalizes the construction of the Thue–Morse sequence to finite alphabets with more than two letters. We show how one can use such partitions to (theoretically!) pour the same volume of coffee from an urn into a finite number of cups so that each cup gets almost the same amount of caffeine.

Full Text (PDF format)

Published 9 December 2015