A Note with Computer Exploration on the Triangle Conjecture

Christophe Cordero (1, 2)

1 Université Gustave Eiffel
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

The triangle conjecture states that codes formed by words of the form a i ba j are either commutatively equivalent to a prefix code or not included in a finite maximal code. Thanks to computer exploration, we exhibit new examples of such non-commutatively prefix codes. In particular, we improve a lower bound in a bounding due to Shor and Hansel. We discuss in the rest of the article the possibility of those codes to be included in a finite maximal code.

Mots clés: Codes; Triangle conjecture; Commutative equivalence conjecture

Domaines: Combinatoire [math.CO]

Christophe Cordero. A Note with Computer Exploration on the Triangle Conjecture. Lecture Notes in Computer Science, 2019, ⟨10.1007/978-3-030-13435-8_30⟩. ⟨hal-03682699⟩