• TUCS Publication Series
• How to Publish in TUCS Series
• Publication Search
• Publication Graph
• Publication Input
• Publication Input Guide
• JuFo Browser

On the Independence of Equations in Three Variables

Tero Harju, Dirk Nowotka, On the Independence of Equations in Three Variables. TUCS Technical Reports 432, Turku Centre for Computer Science, 2001.

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.

Files:

Full publication in PDF-format

BibTeX entry:

@TECHREPORT{tHaNo01a,
  title = {On the Independence of Equations in Three Variables},
  author = {Harju, Tero and Nowotka, Dirk},
  number = {432},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2001},
  keywords = {combinatorics on words, systems of equations, independence},
  ISBN = {952-12-0930-5},
}

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

Edit publication