Repetition avoidance in products of factors

09/05/2018

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by   Pamela Fleischmann, et al.

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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. Moussavi and Shallit obtained that RT_i(2)=2i and RT_2(3)=134. We show that RT_i(3)=3i2+14 if i is even and RT_i(3)=3i2+16 if i is odd and i>3.