Mathematics – Combinatorics
Scientific paper
2003-02-25
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".
Rampersad Narad
Shallit Jeffrey
Wang Ming-wei
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