4 problems

For $k \geq 2$, let $\min S_{\mathrm{sw}}^{(k)}(n)$ denote the minimal subword entropy among words of length $n$. Eventual monotonicity conjecture. There is a value $N$ such that t…

Let $w$ be a binary word of length $n$ achieving the minimal subword entropy. Uniqueness conjecture. There are only finitely many values of $n$ for which such a word $w$ has severa…

For $k \geq 2$, let $w$ be a binary word of length $n \geq 1$ achieving the minimal subword entropy $\min S_{\mathrm{sw}}^{(k)}(n)$. A run is a maximal consecutive block of equal l…

Let $L_2$ denote the asymptotic binary subword-entropy constant, and let $\log_2$ be the logarithm to base $2$. Strict lower-bound conjecture. … This conjecture is supported by exh…