3 problems

A bouquet of convex geometries is the combinatorial structure considered in the paper as a generalization of ideals of convex geometries. Bouquet realizability conjecture. Every bo…

Let a median system be a set system whose 1-inclusion graph is a median graph, and let $d$ denote its dimension. Median-system realization conjecture. Every median system of dimens…

Let $\mathcal{I}=(U,\mathcal{C'})$ be an ideal of a convex geometry, with Euclidean dimension $\operatorname{dim_{\mathbb{E}}}(\mathcal{I})$ and VC-dimension…