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Discrete Math

Product free sets in the alternating group

Noam Lifshitz (IAS)

Location:  Hill Center Room 705
Date & time: Monday, 31 October 2022 at 2:00PM - 3:00PM

Abstract: A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of \(A_n\) be?

In the talk we will completely solve the problem by determining the largest product free subset of \(A_n\).

Our proof combines a representation theoretic argument due to Gowers, with an analytic tool called hypercontractivity for global functions. We also make use of a dichotomy between structure and a pseudorandomness notion of functions over the symmetric group known as globalness.

Based on a joint work with Peter Keevash and Dor Minzer

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