2024/09/18 by Currie, James D., Mol, Lucas, Peltomäki, Jarkko · 2 citations
#68R15 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.2409.12068
In 2017, Vesti proposed the problem of determining the repetition threshold for infinite rich words, i.e., for infinite words in which all factors of length n contain n distinct nonempty palindromic factors. In 2020, Currie, Mol, and Rampersad proved a conjecture of Baranwal and Shallit that the repetition threshold for binary rich words is 2 + √(2)/2. In this paper, we prove a structure theorem for 16/7-power-free ternary rich words. Using the structure theorem, we deduce that the repetition threshold for ternary rich words is 1 + 1/(3 - μ) ≈ 2.25876324, where μ is the unique real root of the polynomial x3 - 2x2 - 1.