The cylindrical width of transitive sets

2021/01/27 by Ashwin Sah, Mehtaab Sawhney, Sah, Ashwin +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG

paper · pdf · doi:10.48550/arxiv.2101.11207

17 pages

arxiv created 2021/01/27 · arxiv updated 2021/01/28

Abstract

We show that for every 1 ≤ k ≤ d/(log d)^C, every finite transitive set of unit vectors in ℝ^d lies within distance O(1/√(log (d/k))) of some codimension k subspace, and this distance bound is best possible. This extends a result of Ben Green, who proved it for k=1.

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