Imre Leader

activity

20242026

most citedTurán Densities for Daisies and Hypercubes

10 citations · 10 across the 6 of their papers we have counts for

collaborators

6 papers

math.AT2026

Antipodal paths in covers of spheres

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

In this note we show that if the sphere $S^{n}$ is covered by $k$ open sets with $n \geq 2 k - 2$ , then one of these sets contains a path with antipodal endpoints. This is best…

math.CO2026

Generalised Prisms and Euclidean Ramsey Theory

Maria-Romina Ivan, Imre Leader, Mark Walters

A finite subset $X$ of $R^{d}$ is called Ramsey if for every $k$ there exists an $n$ such that whenever $R^{n}$ is $k$ -coloured there exists a monochromatic congruent c…

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

Turán 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.CO2024

Block Sizes in the Block Sets Conjecture

Maria-Romina Ivan, Imre Leader, Mark Walters

A set $X$ is called Euclidean Ramsey if, for any $k$ and sufficiently large $n$ , every $k$ -colouring of $R^{n}$ contains a monochromatic congruent copy of $X$ . This notion w…

math.CO2024★ 10 cited

Turán 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. Bollobás, Leader…