The Limit of Repetition Thresholds of Rich Sequences
Abstract
The repetition threshold of a class of sequences is the smallest number $r$ such that a~sequence from the class contains no repetition with exponent $> r$. We focus on the class~$\mathcal{C}_d$ of $d$-ary sequences rich in palindromes. In 2020, Currie, Mol, and Rampersad determined the repetition threshold for $\mathcal{C}_2$. In 2024, Currie, Mol and Peltomäki found the repetition threshold for $\mathcal{C}_3$ and conjectured that the repetition threshold for $\mathcal{C}_d$ tends to~2 with $d$ growing to infinity. Here we verify their conjecture.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
semigroups and automata theory
advanced mathematical theories
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 2
- Publication date
- 23 April 2026
- Language
- EN