Fibonacci prefix antipower conjecture

Let FnF_n be an even Fibonacci number, where the Fibonacci numbers satisfy the usual recurrence, and let f\mathbf{f} denote the Fibonacci word. A kk-antipower is a concatenation of kk pairwise distinct blocks of equal length. Fibonacci prefix antipower conjecture. There is an (Fn1)(F_n-1)-antipower with block length Fn2+Fn1\frac{F_n}{2}+F_{n-1} that is a prefix of f\mathbf{f}. Based on the supplied text, this is an empirical conjecture about explicit antipower prefixes of the Fibonacci word; no resolution is given.

Sources & referencesView supporting material

Primary source

Swapnil Garg, “Antipowers in Uniform Morphic Words and the Fibonacci Word”, arXiv:1907.10816 (2021).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.