6 problems

Let an $m$-distance set be a set of points whose pairwise distances take at most $m$ values. The multiplicity of a distance is the number of unordered pairs of points in the set re…

Let a triangular lattice be the set of points with coordinates $a(1,0)+b(\frac12,\frac{\sqrt3}{2})$, where $a,b\in\mathbb Z$. Consider a regular hexagon or an equiangular hexagon w…

Let a triangular lattice be the set of points with coordinates $a(1,0)+b(\frac12,\frac{\sqrt3}{2})$, where $a,b\in\mathbb Z$. An equiangular hexagon has six sides in the lattice di…

Let a triangular lattice be the set of points with coordinates $a(1,0)+b(\frac12,\frac{\sqrt3}{2})$, where $a,b\in\mathbb Z$. An $m$-distance set is a set of lattice points whose p…

Let an $m$-distance set be a collection of points in the Euclidean plane such that the distances between any two points take at most $m$ possible values. A triangular lattice is th…

Let $\Delta$ be the triangular lattice. A $K_2$-QPDS $S$ in $\Delta$ has an associated hexagonal structure ${\mathcal P}(S)$ whose hexagons have types $1$, $2$, and $3$. Mortar-and…