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Discrete Math

New Results on Projections

Guy Moshkovitz (IAS)

Location:  Hill 705
Date & time: Monday, 03 February 2020 at 2:00PM - 3:00PM

Abstract: What is the largest number of projections onto k coordinates guaranteed in every family of m binary vectors of length n?

This fundamental question is intimately connected with important topics and results in combinatorics and computer science (Turan numbers, the Sauer-Perles-Shelah Lemma, the Kahn-Kalai-Linial Theorem), and is generally wide open.

We (essentially) settle the question for a wide range of parameters: linear k and sub-exponential m.

 Based on joint work with Noga Alon and Noam Solomon.

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