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On the Independence of Equations in Three Variables

Tero Harju, Dirk Nowotka, On the Independence of Equations in Three Variables. Theoretical Computer Science 307(1), 139–172, 2003.

Abstract:

<p>
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.
</p>

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BibTeX entry:

@ARTICLE{jHaNo03b,
  title = {On the Independence of Equations in Three Variables},
  author = {Harju, Tero and Nowotka, Dirk},
  journal = {Theoretical Computer Science},
  volume = {307},
  number = {1},
  pages = {139–172},
  year = {2003},
  keywords = {combinatorics on words, systems of equations, independence},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

Publication Forum rating of this publication: level 2

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