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The Equation aM = bNcP in a Free Semigroup
Tero Harju, Dirk Nowotka, The Equation <i>a<sup>M</sup></i> = <i>b<sup>N</sup>c<sup>P</sup></i> in a Free Semigroup. TUCS Technical Reports 561, Turku Centre for Computer Science, 2003.
Abstract:
The equation <i>a<sup>M</sup></i> = <i>b<sup>N</sup>c<sup>P</sup></i>
has only periodic solutions in a free semigroup. This result was first
proven by Lyndon and Schützenberger.
We present a very short
proof of this classical result. Moreover, we establish
that the power of two or more of a primitive
word cannot be factorized into conjugates of a different word.
Files:
Abstract in PDF-formatBibTeX entry:
@TECHREPORT{tHaNo03c,
title = {The Equation aM = bNcP in a Free Semigroup},
author = {Harju, Tero and Nowotka, Dirk},
number = {561},
series = {TUCS Technical Reports},
publisher = {Turku Centre for Computer Science},
year = {2003},
keywords = {combinatorics on words, free semigroup, word equations},
ISBN = {952-12-1246-2},
}
Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics