2003/02/25 by Narad Rampersad, Jeffrey Shallit, Rampersad, Narad +4
Computer Science · Mathematics · #68R15 #Algorithms and Data Compression #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO #msc:68R15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0302303
PLEASE NOTE: After this paper was prepared, we learned that all our results appeared (albeit with different proofs) in a paper of F. M. Dekking, On repetitions of blocks in binary sequences, J. Combin. Theory Ser. A 20 (1976), 292--299
openalex publication_date 2003/02/25 · arxiv created 2003/04/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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".