3 problems

Let a run be a maximal repetition in a word. For a word of length $n$, the maximal number of runs is linear in $n$. Kolpakov–Kucherov conjecture. The maximal number of runs in a wo…

For a word of length $n$, let $\rho(n)$ denote the maximum number of runs, where a run is a periodic factor whose length is at least twice its period. Runs conjecture. The maximum…

Let a run be a maximal repetition in a string, and let $c$ be a constant such that every string of length $n$ has at most $cn$ runs. For binary alphabets, computations had supporte…