5 problems

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

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 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: