Radon numbers grow linearly

DOI10.1007/S00454-021-00331-2arXiv1912.02239MaRDI QIDQ6330451

Publication date: 4 December 2019

Abstract: Define the

k

-th Radon number

r_{k}

of a convexity space as the smallest number (if it exists) for which any set of

r_{k}

points can be partitioned into

k

parts whose convex hulls intersect. Combining the recent abstract fractional Helly theorem of Holmsen and Lee with earlier methods of Bukh, we prove that

r_{k}

grows linearly, i.e.,

r_{k} l e c (r_{2}) c d o t k

.

Mathematics Subject Classification ID

Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Helly-type theorems and geometric transversal theory (52A35)

This page was built for publication: Radon numbers grow linearly

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6330451)