We prove a 2018 conjecture of Krawchuk and Rampersad on the extremal behavior of $c(n)$, where $c(n)$ counts the number of length-$n$ factors of the Thue-Morse word $\mathbf{t}$, up to cyclic rotation.
翻译:我们证明2018年Krawchuk和Rampersad 的推测,其极端行为为$c(n)美元,其中,$c(n)美元等于Thue-Morse word $\mathbf{t}的长度-n美元系数数,直至循环周期。