Just checked with AI: Thue showed 1906 that there are infinitely many square free words (:= a word that doesn't contain a non-primitive word) over an alphabet with at least 3 symbols.
On p.2 they follow my idea of adding the lowest possible letter at the end, although they generalise it to adding the letter as close to the end as possible. They conjecture that this process does not stop. I'm always amazed with combinatorics how quickly you arrive at questions that no one knows the answer to.
n4r9|6 months ago
On p.2 they follow my idea of adding the lowest possible letter at the end, although they generalise it to adding the letter as close to the end as possible. They conjecture that this process does not stop. I'm always amazed with combinatorics how quickly you arrive at questions that no one knows the answer to.