7 problems

Let a triangular lattice be the set of points with coordinates $a(1,0)+b(\frac12,\frac{\sqrt3}{2})$, where $a,b\in\mathbb Z$. A regular hexagon has six equal side lengths, and a…

For each value of $m$ in the comparison table, let the corresponding hexagon construction mean the set of triangular-lattice points obtained from the regular or equiangular hexagon…

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 $\Omega\subset\mathbb{R}^2$ be a domain, let $2<p\leq\infty$, and let $\mu$ be an atomic measure with $\mu(\Omega)=|\Omega|$. For $2<p<\infty$, define $\mathcal{A}^p(\mu)$ by…

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…