About Duval's conjecture

: Harju T, Nowotka D

: 2003

Lecture Notes in Computer Science

DEVELOPMENTS IN LANGUAGE THEORY, PROCEEDINGS

: LECT NOTES COMPUT SC

: 2710

: 316

: 324

: 9

: 3-540-40434-1

: 0302-9743

A word is called unbordered if it has no proper prefix which is also a suffix of that word. Let mu(w) denote the length of the longest unbordered factor of a word w. Let a word where the longest unbordered prefix equal to mu(w) be called Duval extension. A Duval extension is called trivial, if its longest unbordered factor is of the length of the period of that Duval extension. In 1982 it was shown by Duval that every Duval extension w longer than 3mu(w)-4 is trivial. We improve that bound to 5mu(w)/2-1 in this paper, and with that, move closer to the bound 2mu(w) conjectured by Duval. Our proof also contains a natural application of the Critical Factorization Theorem.

Mathematics