3 problems

Let $\varLambda\subset\mathbb R^3$ be a Delone set. A set of $\varLambda$-directions is in general position when any three directions from it span the whole $3$-space. Seven-direct…

Let $n\ge 3$, let $N=[n,2]$, and let $m_n$ denote the minimum number of pairwise nonparallel $\varLambda$-directions whose X-rays determine every convex subset of a strong $n$-cycl…

Let row sums be $\mathcal{R}=(r_1,r_2,\ldots,r_m)$ and column sums be $\mathcal{C}=(c_1,c_2,\ldots,c_n)$, where … and … Assume that the line sums are consistent. Small-boundary rec…