New Bounds on Antipowers in Binary Words

12/17/2019

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by   Lukas Fleischer, et al.

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Fici et al. defined a word to be a k-power if it is the concatenation of k consecutive identical blocks, and an r-antipower if it is the concatenation of r pairwise distinct blocks of the same size. They defined N(k, r) as the shortest length l such that every binary word of length l contains either a k-power or an r-antipower. In this note we obtain some new upper and lower bounds on N(k, r).