5 problems

A cyclic $(n_k)$ configuration is a cyclic configuration in which every point lies on $k$ lines and every line contains $k$ points. Unsplittability conjecture. All cyclic $(n_k)$ c…

Let $\mathrm{GR}(21_4)$ be the Grünbaum–Rigby configuration, decomposed into subconfigurations $\mathrm S_{12}$, $\mathrm S_{13}$, and $\mathrm S_{23}$ with point orbits…

Let $A\subset\mathbb{R}^2$ be a set of positive upper density, and let $u,v,w\in\mathbb{R}^2$ be non-collinear points. A configuration congruent to a finite set means an image of t…

Classification conjecture. A cyclic $(n_3)$ configuration is unsplittable if and only if its Levi graph belongs to one of the following three infinite families:

An $n_3$-configuration is a $3$-uniform configuration with $n$ points and $n$ lines, in which every point lies on three lines and every line contains three points. Call such a conf…