Geodesic
Antipowers in Uniform Morphic Words and the Fibonacci Word
Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3.

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Fici, Restivo, Silva, and Zamboni define a $k$-antipower to be a word composed of $k$ pairwise distinct, concatenated words of equal length. Berger and Defant conjecture that for any sufficiently well-behaved aperiodic morphic word $w$, there exists a constant $c$ such that for any $k$ and any index $i$, a $k$-antipower with block length at most $ck$ starts at the $i$th position of $w$. They prove their conjecture in the case of binary words, and we extend their result to alphabets of arbitrary finite size and characterize those words for which the result does not hold. We also prove their conjecture in the specific case of the Fibonacci word.
DOI : 10.46298/dmtcs.7134
Classification : 68R15 
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     title = {Antipowers in {Uniform} {Morphic} {Words} and the {Fibonacci} {Word}},
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Garg, Swapnil. Antipowers in Uniform Morphic Words and the Fibonacci Word. Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3. doi : 10.46298/dmtcs.7134. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.7134/

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