6 problems

Let $\mathfrak{h}$ be a unit-area $1$-LQG sphere independent of the three whole-plane space-filling curves $(\eta^{\mathrm{b}},\eta^{\mathrm{r}},\eta^{\mathrm{g}})$ obtained from t…

Weak-limit conjecture. The unique maximal Schnyder wood of the UIHPT is the weak limit of the maximal Schnyder wood of a uniformly random triangulation from $\cT_n^m$ as…

The twenty-vertex model is the model associated with Schnyder woods on the regular triangular lattice, where each vertex has in-degree and out-degree $3$; its flow lines are define…

Let $G$ be a triangulation on a genus $g\geq 1$ orientable surface. An orientation of $G$ has vertex outdegree divisible by $3$ and at least $3$ when every vertex has outdegree div…

Let $G$ be a map on a genus $g\geq 1$ orientable surface. An edge, positive-vertex, positive-face angle labeling means a labeling with the edge condition and positive vertex and fa…

Let $G$ be a map on a genus $g\geq 1$ orientable surface. A 1-edge, positive-vertex, 1-face angle labeling means a labeling with the edge, vertex, and face conditions indicated by…