7 problems

Shortest common superpattern conjecture. For any $l\ge 1$,

Layered extremal word conjecture. If $\Pi$ is a set of layered patterns, then

Folded-form tightness conjecture. The construction's upper bound is tight:

Let $P$ be an avoidable pattern, meaning that some alphabet admits arbitrarily long words avoiding $P$. For a fixed alphabet, an extremal $P$-avoiding word is a word that avoids…

For each positive integer $m$, let $\mathcal E_m$ be the set of exceptional normalized words of length $m$, and let $\mathcal{NW}_m$ be the set of normalized words of length $m$. H…

Let $w$ be a word, and let $\langle w\rangle_{\operatorname{\mathsf{hare}}}$ and $\langle w\rangle_{\operatorname{\mathsf{tortoise}}}$ denote its hare- and tortoise-fertilities. Th…

Let $w$ be a word of length $m$, and let $\langle w\rangle_{\operatorname{\mathsf{hare}}}$ and $\langle w\rangle_{\operatorname{\mathsf{tortoise}}}$ denote its hare- and tortoise-f…