2013 Unit Vectors in the Plane
Imre Barany, Boris D. Ginzburg, and Victor S. Grinberg
TL;DR
This paper proves that for any norm on the plane and any set of 2013 unit vectors, there exists a signed sum of these vectors with a norm not exceeding one.
Contribution
It establishes a universal bound for signed sums of a large set of unit vectors in any plane norm, extending previous results.
Findings
Existence of a signed sum with norm ≤ 1 for 2013 unit vectors in any plane norm.
The bound applies universally regardless of the specific norm or vectors.
Provides a new insight into vector sums in geometric functional analysis.
Abstract
Given a norm on the plane and 2013 unit vectors in this norm, there is a signed sum of these vectors whose norm is at most one.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · Mathematics and Applications