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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 is covered by open sets with , 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 of is called Ramsey if for every there exists an such that whenever is -coloured there exists a monochromatic congruent c…