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On Hypercube Statistics

Introductory Workshop - Graph Theory: Extremal, Probabilistic and Structural February 10, 2025 - February 14, 2025

February 10, 2025 (03:30 PM PST - 04:15 PM PST)
Speaker(s): Noga Alon (Princeton University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

On Hypercube Statistics

Abstract

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For a subset A of vertices of the n-dimensional cube Q_n, let lambda(n,d,s,A) denote the fraction of d-dimensional subcubes of Q_n that contain exactly s points of A. Let lambda(n,d,s) denote the maximum possible value of lambda(n,d,s,A), as A ranges over all subsets of vertices of Q_n, and let lambda(d,s) denote the limit of this quantity as n tends to infinity. I will discuss the problem of determining or estimating the quantities lambda(d,s), describing several intriguing conjectures and some (modest) results. Joint work with Maria Axenovich and John Goldwasser.

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On Hypercube Statistics

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