David Ellis

works on

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

From the 1 of 4 linked papers with an AI index.

activity

20242026

collaborators

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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…

math.CO2024

TurÃ¡n Densities for Daisies and Hypercubes

David Ellis, Maria-Romina Ivan, Imre Leader

An $r$ -daisy is an $r$ -uniform hypergraph consisting of the six $r$ -sets formed by taking the union of an $(r - 2)$ -set with each of the 2-sets of a disjoint 4-set. BollobÃ¡s, Leader…