Article ID Journal Published Year Pages File Type
6876299 Theoretical Computer Science 2013 14 Pages PDF
Abstract
Eugène Prouhet is considered to be one of the fathers of combinatorics on words. In his pioneering work, he constructed a solution to the equal powers problem in number theory (later known as the Prouhet-Tarry-Escott problem) based on positions of symbols in words obtained by iteration of a uniform endomorphism of the free monoid over a finite alphabet. We show that composition of uniform morphisms of free monoids is a fairly powerful tool to obtain solutions to a more general problem, which covers the major generalizations of Prouhet's theorem appearing in literature.
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Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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