17 problems

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

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 $G$ 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…

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 $M$ 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 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 $\mathfrak{P}=(\Sigma,R,\{abc\})$, where … For words $w,w'\in\Sigma^*$, let $d(w,w')$ denote their distance, and let an irreducible transformation of order at most two mean an…

Let $\mathfrak{P}=(\Sigma,R,C)$ be a Parikh rewriting system, and suppose that $w\Rightarrow_{\mathfrak{P}}w'$ has a sequence of irreducible transformations as in Theorem, of lengt…

Let $\mathfrak{P}$ be the Parikh rewriting system considered for the ternary alphabet, and let the order of an irreducible transformation denote its order in the system. An irreduc…

Let $(\mathcal{S},\mathcal{R})$ be an Artin–Tits presentation, and let denote the reducing equivalence defined earlier in the paper. Reducing conjecture. Every Artin–Tits presentat…

Plain-group characterization conjecture. The following assertions are equivalent: