32 problems

Let $G$ be a hyperbolic one-relator group. Wise's conjecture. Every such group is virtually free-by-cyclic. If true, this would imply that every hyperbolic one-relator group admits…

Convergence conjecture. This rewriting system is convergent, meaning that it is terminating and confluent.

The discussion concerns a family of $4$-dimensional resource-management cells arising from local computations on proofs, including cells for a weakening followed by a contraction,…

Converse property. If $f$ and $g$ are two parallel $2$-arrows in $\langle \Sigma \rangle$ such that $\overline{\pi}(f)=\overline{\pi}(g)$, then

Nonexistence conjecture. For any given surface $F$, there does not exist a set of terminal and confluent reduction rules with these properties. A proof would rule out this proposed…

Madlener–Otto conjecture. A group admits a finite confluent length-reducing rewriting system if and only if it is plain.

Conjecture. For every $a\in\mathbb{C}^4$, the following are equivalent: the properad $\mathcal{P}_a$ induces a confluent system; the morphism $\varphi_a$ is a bijection in weight…

Immortality-equivalence conjecture. The following properties of an amoeba $A$ are equivalent:

Let an inverse-closed finite convergent length-reducing rewriting system present a group. A group is plain if it is a free product of finitely many finite groups and finitely gener…

Let $G$ be a group. Say that $G$ is plain if it is isomorphic to a free product of finitely many finite groups and finitely many copies of $\mathbb Z$. A finite convergent length-r…

A one-relation monoid is a monoid given by a finite presentation with one defining relation. A finite complete rewriting system is a finite rewriting system that is both terminatin…

Completeness conjecture for generalized controlled-not identities. These identities are complete for $\operatorname{Iso}(\mathsf{FinSet}_2)$: every equality of Boolean isomorphisms…

Let $G$ be a group. A finite convergent length-reducing rewriting system for $G$ is a presentation $(\Sigma,T)$ by such a system. Madlener–Otto conjecture. $G$ admits a finite conv…

Let $G$ be a group. A finite convergent length-reducing rewriting system for $G$ is a presentation $(\Sigma,T)$ by such a system, where each rewriting rule has a right-hand side of…

Let $\mathbf{Mag}^{\{3,4\}}$ be the quotient of the magmatic operad by the relations represented by the arity-$3$ and arity-$4$ trees. Consider the displayed rewrite rules, includi…

Let $\mathbf{CAs}^{\left(\gamma\right)}$ be the higher comb associative operad, let $\mathbf{Mag}$ be the magmatic operad of trees, and consider rewrite presentations whose left- a…

Let $\mathbf{CAs}^{\left(\gamma\right)}$ denote the higher comb associative operad associated with $\gamma$, and let the algorithm described in the paper be the completion algorith…

Let $(\Sigma,T)$ be a finite, monadic, confluent rewriting system presenting a group $G$. A plain group is a free product of a finitely generated free group with finitely many fini…

Let $M$ be an Artin–Tits monoid. A padding of a multifraction is obtained by inserting an even number of trivial components at its beginning; semi-convergence up to $f$-padding mea…

Let $M$ be an Artin–Tits monoid, and let $\mathcal{R}$-reduction be the reduction system on multifractions associated with $M$. Conjecture A. $\mathcal{R}$-reduction is semi-conver…

Let $M$ be a gcd-monoid, let $\mathcal{R}_{M}$ be its reduction system, and let an $n$-multifraction be a multifraction with $n$ entries. A reduction sequence is a sequence of elem…

Let $M$ be an Artin–Tits monoid, let $\mathcal{F}_{M}$ be the set of multifractions over $M$, and let $\operatorname{red}_{\mathrm{t}}$ denote tame reduction. A multifraction is un…

Let $M$ be an Artin–Tits monoid and let $\mathcal{R}_{M}$ be its reduction system on multifractions. The system is uniformly cross-confluent if there is a map $\nabla$ from multifr…

Let $M$ be an Artin–Tits monoid and let $\mathcal{R}_{M}$ be its reduction system on multifractions. Two multifractions are right reducts of the same multifraction if they are obta…

Let $\langle S,R\rangle$ be an Artin–Tits presentation, let $w\in S\cup S^{-1}$ be a word, and write $\overline{w}$ for the group element represented by $w$. Let…