David Ellis

works on

antipodal paths 1 combinatorial topology 1 hypercube edge-colouring 1 open covers 1 sphere coverings 1

From the 1 of 3 linked papers with an AI index.

collaborators

3 papers

math.AT2026

Antipodal paths in covers of spheres

David Ellis, Maria-Romina Ivan, Imre Leader +1

The authors prove that if an n‑dimensional sphere is covered by k open sets with n ≥ 2k‑2, then one of the sets must contain a path whose endpoints are antipodal, and they show thi…

math.CO2025

TurÃ¡n Densities for Small Hypercubes

David Ellis, Maria-Romina Ivan, Imre Leader

How small can a set of vertices in the $n$ -dimensional hypercube $Q_{n}$ be if it meets every copy of $Q_{d}$ ? The asymptotic density of such a set (for $d$ fixed and $n$ large) is den…

math.CO2025

The Maximum Number of Bases in a Family of Vectors

David Ellis, Maria-Romina Ivan, Imre Leader

The proportion of $d$ -element subsets of $F_{2}^{d}$ that are bases is asymptotic to $\prod_{j = 1}^{\infty} (1 - 2^{- j}) \approx 0.29$ as $d \to \infty$ . It is natural to ask whet…