8 problems

Let $w$ be a string of length $n$, and let $w'$ be obtained from $w$ by an edit operation. Write $\chi(w)$ for the size of a smallest suffixient set of $w$. The additive sensitivit…

Higher-arity diameter conjectures. For sufficiently long strings, the diameters of 3-ary, 4-ary, and 5-ary strings are respectively

Ternary diameter conjecture.

Greedy common-superstring conjecture. Greedy produces a common superstring $t'$ of length at most $2s$.

Let $w$ be a string and let $w'$ result from applying one of the string operations considered in the paper, including edits, rotations, and reversals. The multiplicative sensitivit…

Let a Fibonacci word be a finite word in the Fibonacci-word sequence, and let a net occurrence be an occurrence of a repeated string with unique left and right extensions. Fibonacc…

Let $\rho(n)$ be the maximum number of runs that can occur in a word of length $n$. Runs Conjecture. For every positive integer $n$, … The conjecture concerns the linear upper boun…

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…