Squarefree words with interior disposable factors

Abstract

We give a partial answer to a problem of Harju by constructing an infinite ternary squarefree word $w$ with the property that for every $k\ge 3312$ there is an interior length-$k$ factor of $w$ that can be deleted while still preserving squarefreeness. We also examine Thue's famous squarefree word (generated by iterating the map $0\to 012$, $1\to 02$, $2\to 1$) and characterize the positions $i$ for which deleting the symbol appearing at position $i$ preserves squarefreeness.

10 pages