On gapped repeats in a cyclic Fibonacci word
arXiv:2606.0207138.5
AI Analysis
Provides a combinatorial characterization for a specific cyclic word, which is incremental for the field of combinatorics on words.
The authors characterize pairs of indices where length-s subwords of a cyclic Fibonacci word are equal, and count such pairs.
In this article, we consider the words with cyclic indices. For given $s$, we consider the pair $(ι,κ)$ of indices such that the word of length $s$ from $ι$ is equal to the word of length $s$ from $κ$. We give a characterization of such pairs for a cyclic Fibonacci word, and give the number of them.