Geodesic
Product mixing in the alternating group
Discrete analysis (2016) Cet article a éte moissonné depuis la source Scholastica

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We prove the following one-sided product-mixing theorem for the alternating group: Given subsets $X,Y,Z \subset A_n$ of densities $α,β,γ$ satisfying $\min(αβ,αγ,βγ)\gg n^{-1}(\log n)^7$, there are at least $ (1+o(1))αβγ|A_n|^2$ solutions to $xy=z$ with $x\in X, y\in Y, z\in Z$. One consequence is that the largest product-free subset of $A_n$ has density at most $n^{-1/2}(\log n)^{7/2}$, which is best possible up to logarithms and improves the best previous bound of $n^{-1/3}$ due to Gowers. The main tools are a Fourier-analytic reduction noted by Ellis and Green to a problem just about the standard representation, a Brascamp--Lieb-type inequality for the symmetric group due to Carlen, Lieb, and Loss, and a concentration of measure result for rearrangements of inner products.
Publié le : 
@article{DAS_2016_a17,
     author = {Sean Eberhard},
     title = {Product mixing in the alternating group},
     journal = {Discrete analysis},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2016_a17/}
}
TY  - JOUR
AU  - Sean Eberhard
TI  - Product mixing in the alternating group
JO  - Discrete analysis
PY  - 2016
UR  - http://geodesic.mathdoc.fr/item/DAS_2016_a17/
LA  - en
ID  - DAS_2016_a17
ER  - 
%0 Journal Article
%A Sean Eberhard
%T Product mixing in the alternating group
%J Discrete analysis
%D 2016
%U http://geodesic.mathdoc.fr/item/DAS_2016_a17/
%G en
%F DAS_2016_a17
Sean Eberhard. Product mixing in the alternating group. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a17/