9 problems

Uniqueness conjecture. This bi-infinite caterpillar is the unique bi-infinite fully leafed caterpillar of $P2$-graphs.

Consider the sea grafting (g) shown in Figure of the paper. A bi-infinite fully leafed caterpillar is a fully leafed caterpillar that extends infinitely in both directions. Extenda…

Let a Penrose P2 tiling be a tiling by kites and darts, and consider its fully leafed induced subcaterpillars, meaning fully leafed induced subtrees whose underlying tree is a cate…

Let the $3,5,3 honeycomb be a tessellation of$operatorname{mathbb{H}}^3…

The $3,5,3 honeycomb is a hyperbolic honeycomb in$operatorname{mathbb{H}}^3…

Let $T_1$, $T_2$, and $T_3$ be the three Penrose tilings considered in the paper, and let $\operatorname{dim}_{\mathrm{B}}$ and $\operatorname{cap}$ denote box-counting dimension a…

Let $T_1$, $T_2$, and $T_3$ be the three Penrose tilings considered in the paper, and let $\operatorname{Sp}(\Delta_{T_i})$ denote the spectrum of the graph Laplacian of $T_i$. Pen…

Let $C$ be a Penrose caterpillar, let $S$ be the graded poset of caterpillars used in the source, and let $f_{boat}$ transform a Penrose caterpillar by replacing each relevant subp…

Let $T$ be a fully leafed Penrose subtree. A Penrose tree is saturated if $n_{1}(T)=\overline{L_{P2}}(n(T))$, where $\overline{L_{P2}}(n)=8n/17+b$ is the unique linear upper bound…