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A counterexample to the triangle conjecture. (English) Zbl 0558.20032
It is known that the triangle conjecture sets a bound on the cardinality of a code formed by words of the form \(a^iba^j\). A counterexample exceeding this bound is presented in this paper. This also disproves a stronger conjecture that every code is commutatively equivalent to a prefix code.

94A45 Prefix, length-variable, comma-free codes
05A99 Enumerative combinatorics
Full Text: DOI
[1] de Felice, C, On the triangle conjecture, Inform. process. lett., 14, 197-200, (1982) · Zbl 0487.68074
[2] Hansel, G, Baïonnettes et cardinaux, Discrete math., 39, 331-335, (1982) · Zbl 0486.20032
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[5] Pin, J.E; Simon, I, A note on the triangle conjecture, J. combin. theory ser. A, 32, 106-109, (1982) · Zbl 0472.05010
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