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Mathematica in research of avoidable patterns in strings

V. Keränen
Journal / Anthology

Mathematics with Vision: Proceedings of the First International Mathematica Symposium
Year: 1995
Page range: 259-266

The new possibilities for the research of avoidable regularities in strings (words), offered by Mathematica, are discussed. In addition to the fact that Mathematica is very well suited to prototyping, the syntax and structures of Mathematica allow us to write efficient codes for conducting quite extensive experiments concerning abelian square-free strings. Moreover, the symbolic computing and pattern matching facilities of Mathematica make it very convenient for writing short programs for finding various kinds of patterns in strings. Our special emphasis in this paper is the avoidability of abelian repetitions. In the case of a four letter alphabet, we present the abelian square-free endomorphism (found in Keranen [4]) which gives the only method that is currently known for constructing arbitrarily long strings over four letters without any abelian squares. Related open problems are discussed.

*Mathematics > Discrete Mathematics > Coding Theory