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# Journal of Combinatorics

## Volume 7 (2016)

### Number 1

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

Pages: 117 – 133

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

#### Authors

#### 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.