Cubefree binary words avoiding long squares

Details Cubefree binary words avoiding long squares Cubefree binary words avoiding long squares

2003-02-25

arxiv.org/abs/math/0302303v2

Mathematics

Combinatorics

PLEASE NOTE: After this paper was prepared, we learned that all our results appeared (albeit with different proofs) in a paper

Scientific paper

Entringer, Jackson, and Schatz conjectured in 1974 that every infinite cubefree binary word contains arbitrarily long squares. In this paper we show this conjecture is false: there exist infinite cubefree binary words avoiding all squares xx with |x| >= 4, and the number 4 is best possible. However, the Entringer-Jackson-Schatz conjecture is true if "cubefree" is replaced with "overlap-free".

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