2 problems

Let $\mathrm{HB}_k(n)$ be the maximum length of an unbordered partial word with parameter $n$ over an alphabet of size $k$, and let $\mathrm{HB}_\infty(n)$ denote the corresponding…

Let $\mathrm{HB}_3(n)$ denote the maximum length of an unbordered partial word of length parameter $n$ over an alphabet of size $3$. Monotonicity conjecture for $\mathrm{HB}_3$. Fo…