### Upper bound for the number of closed and privileged words. (arXiv:1911.11197v1 [cs.DM])

A non-empty word $w$ is a border of the word $u$ if $\vert w\vert<\vert u\vert$ and $w$ is both a prefix and a suffix of $u$. A word $u$ with the border $w$ is closed if $u$ has exactly two occurrences of $w$. A word $u$ is privileged if $\vert u\vert\leq 1$ or if $u$…