The Prouhet-Tarry-Escott Problem and Generalized Thue-Morse Sequences

TL;DR

This paper introduces new methods for generating Prouhet-Tarry-Escott partitions of arbitrary regularity, generalizing the Thue-Morse sequence to larger alphabets, with theoretical applications to evenly distributing quantities like caffeine.

Contribution

It presents novel techniques for creating Prouhet-Tarry-Escott partitions and extends the Thue-Morse sequence to finite alphabets beyond two letters.

Findings

New methods for large regularity partitions

Generalization of Thue-Morse sequence to multiple alphabets

Theoretical application to even distribution problems

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 coffee from an urn into a finite number of cups so that each cup gets almost the same amount of caffeine.