Minimal critical exponent of quasiperiodic words
Résumé
A quasiperiodic word is a finite or infinite word that can be obtained by concatenations or overlaps of a given finite word. We proved that the least critical exponent of a quasiperiodic binary word is 7/3. For larger alphabets, given any e>0, we provide a construction of a ternary quasiperiodic word with critical exponent 2 +e.