On the independence of equations in three variables.

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Harju, Tero and Nowotka, Dirk (2003) On the independence of equations in three variables. Theoretical Computer Science, 307 (1). pp. 139-172. DOI 10.1016/S0304-3975(03)00098-7.

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Abstract

We prove that an independent system of equations in three variables with a nonperiodic solution and at least two equations consists of balanced equations only. For that, we show that the intersection of two different entire systems contains only balanced equations, where an entire system is the set of all equations solved by a given morphism. Furthermore, we establish that two equations which have a common nonperiodic solution have the same set of periodic solutions or are not independent.

Document Type: Article
Keywords: combinatorics on words systems of equations independence
Research affiliation: Kiel University
Refereed: Yes
Date Deposited: 12 Feb 2013 16:51
Last Modified: 23 Sep 2019 18:27
URI: https://oceanrep.geomar.de/id/eprint/20291

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