Noam Lifshitz, Product free sets in the alternating group

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.

IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail:, Fax: +82-42-878-9209
Copyright © IBS 2018. All rights reserved.