A1 Refereed original research article in a scientific journal
On the equation x(k) = z(1)(k1) z(2) (k2)...z(n)(kn) in a free semigroup
Authors: Harju T, Nowotka D
Publisher: ELSEVIER SCIENCE BV
Publication year: 2005
Journal:Theoretical Computer Science
Journal name in sourceTHEORETICAL COMPUTER SCIENCE
Journal acronym: THEOR COMPUT SCI
Volume: 330
Issue: 1
First page : 117
Last page: 121
Number of pages: 5
ISSN: 0304-3975
DOI: https://doi.org/10.1016/j.tcs.2004.09.012
Abstract
Word equations of the form x(k) = z(1)(k1) z(2)(k2) ... z(n)(kn) are considered in this paper. In particular, we investigate the case where x is of different length than z(i), for any i, and k and k(i) are at least 3, for all 1 less than or equal to i less than or equal to n, and n less than or equal to k. We prove that for those equations all solutions are of rank 1, that is. x and Z(i) are powers of the same word for all 1 less than or equal to i less than or equal to n. It is also shown that this result implies a well-known result by Appel and Djorup about the more special case where k(i) = k(j) for all 1 less than or equal to i < j less than or equal to n. (C) 2004 Published by Elsevier B.V.
Word equations of the form x(k) = z(1)(k1) z(2)(k2) ... z(n)(kn) are considered in this paper. In particular, we investigate the case where x is of different length than z(i), for any i, and k and k(i) are at least 3, for all 1 less than or equal to i less than or equal to n, and n less than or equal to k. We prove that for those equations all solutions are of rank 1, that is. x and Z(i) are powers of the same word for all 1 less than or equal to i less than or equal to n. It is also shown that this result implies a well-known result by Appel and Djorup about the more special case where k(i) = k(j) for all 1 less than or equal to i < j less than or equal to n. (C) 2004 Published by Elsevier B.V.
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