Correlations of minimal forbidden factors of the Fibonacci word

TL;DR

This paper characterizes the pairwise correlations between minimal forbidden factors of the infinite Fibonacci word, providing insights into their overlap structures and combinatorial properties.

Contribution

It introduces a characterization of correlations among minimal forbidden factors specifically for the Fibonacci word, advancing understanding of its combinatorial structure.

Findings

Correlation patterns among Fibonacci minimal forbidden factors are explicitly described.

The results reveal structural properties of overlaps in Fibonacci words.

Insights may aid in enumeration and pattern avoidance analysis.

Abstract

If $u$ and $v$ are two words, the correlation of $u$ over $v$ is a binary word that encodes all possible overlaps between $u$ and $v$. This concept was introduced by Guibas and Odlyzko as a key element of their method for enumerating the number of words of length $n$ over a given alphabet that avoid a given set of forbidden factors. In this paper we characterize the pairwise correlations between the minimal forbidden factors of the infinite Fibonacci word.