Séminaire Lotharingien de Combinatoire, B22h (1989), 8 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 414/S-22, p.
81-88.]
Pavel Goralcik
Avoidable Words and Lattice Universal Semigroup Varieties
Abstract.
The "purely speculative field" opened to mathematical research by Axel
Thue about 80 years ago - combinatorics of words - has found
many applications since. The original problem of avoidance of squares
in arbitrarily long words on a small (ternary) alphabet continues to
be a source of inspiration. The notion was recently generalized by
Bean, Ehrenfeucht, and McNulty
to the problem of avoidance of an arbitrary word. In this form the
problem perfectly fits into the framework of universal algebra. The
idea goes back to the application of square-free
words to semigroup varieties by Burris, Nelson, and Jezek.
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