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
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