All Questions

Let $T$ be a finite set of tiles in $\mathbb{R}^d$. A tiling of $\mathbb{R}^d$ by $T$ is a collection of disjoint translates of tiles in $T$ whose union is $\mathbb{R}^d$. A tiling is $k$-chromatic if ...

Let a uniform tiling be defined by a vertex configuration $(n_1.n_2.\cdots.n_k)^m$, which is either spherical, Euclidean or hyperbolic. Assume that the tiling is vertex-transitive, especially that ...

The concepts of being non-periodic and aperiodic for tilings have obvious versions for connected graphs with a countable set of vertices and a finite number of edges meeting at each vertex. A graph $G$...

Question: how does one enumerate all star-convex $2n$-vertex sublattices of the plane that have the unique domino-tiling property? Definitions: A subset $S$ of the $xy$-plane is star-convex if there ...

A monomer-dimer tiling of a rectangular grid with $r$ rows and $c$ columns satisfies the tatami condition if no four tiles meet at any point. (Or you can think of it as the removal of a matching from ...