12 problems

A positive frieze of type $(3,8)$ is a positive frieze with parameters $(3,8)$. Fontaine–Plamondon's conjecture. There are exactly $26952$ positive friezes of type $(3,8)$. This en…

Two-parameter family conjecture. There should be a two-parameter family of 4-periodic $E_8$ friezes containing the two one-parameter families given in the paper.

Let ${\rm Frieze}(n)$ denote the set of all arithmetic Coxeter frieze patterns of width $n$, and let ${\rm YFrieze}(n)$ denote the set of all arithmetic Y-frieze patterns of width…

General counting conjecture. If $\gcd(k,w+k+1)=1$, then the number of tame $\operatorname{SL}_k$-frieze patterns of width $w$ over $K$ is

A multidimensional frieze pattern is the collection associated with a Farey polyhedron, consisting of its boundary data together with the $bb$-length function on pairs of vertices.…

Conjecture. Every Y-frieze pattern of width $r$ arises from a Coxeter frieze pattern of width $r$ as in Theorem A.

Positivity conjecture. The only frieze patterns of Type $\Lambda_{p_1,\ldots,p_s}$ with negative entries are those which fail the realizability test. In particular, all quotient di…

Let $\zeta\in\mathbb{C}$ be a root of unity, and consider frieze patterns over the ring $\mathbb{Z}[\zeta]$. Fontaine's finiteness conjecture. For every given height, there are onl…

Coxeter's conjecture. Friezes of order $n$ are in bijection with triangulations of a convex $n$-gon.

Let a tame integral positive $\operatorname{SL}_3$-frieze be a tame frieze pattern whose entries are nonnegative integers and whose adjacent $3\times3$ minors have determinant $1$;…

Realization conjecture. Every frieze pattern of type $D_N$ is of the form $F(\widetilde{\mathcal T})$ for some tagged triangulation $\widetilde{\mathcal T}$ of $S_{\odot}$.

Coincidence conjecture. For every tagged triangulation $\widetilde{\mathcal T}$ of $S_{\odot}$, the frieze patterns coincide: