Repetition avoidance in products of factors

2018/09/05 by Pamela Fleischmann, Pascal Ochem, Fleischmann, Pamela +3
Computer Science · Mathematics · #semigroups and automata theory #Algorithms and Data Compression #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1809.01426

Abstract

We consider a variation on a classical avoidance problem from combinatorics on words that has been introduced by Mousavi and Shallit at DLT 2013. Let pexp_i(w) be the supremum of the exponent over the products of i factors of the word w. The repetition threshold RT_i(k) is then the infimum of pexp_i(w) over all words w∈Σ^ω_k. Mousavi and Shallit obtained that RT_i(2)=2i and RT₂(3)=\tfrac134. We show that RT_i(3)=\tfrac3i2+\tfrac14 if i is even and RT_i(3)=\tfrac3i2+\tfrac16 if i is odd and i≥3.

Related

• Repetition Avoidance in Circular Factors
• Repetition factorization of automatic sequences
• The repetition threshold for ternary rich words
• The spectrum of the exponents of repetition
• A Generalization of Repetition Threshold