Geodesic
Sumsets as unions of sumsets of subsets
Discrete analysis (2017) Cet article a éte moissonné depuis la source Scholastica

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Let $S$ and $T$ be subsets of $\mathbf{F}_q^n$. We show there are subsets $S'$ of $S$ and $T'$ of $T$ such that $S+T$ is the union of $S+T'$ and $S'+T$, with $|S'| + |T'|$ bounded by $c^n$ with $c q$. The proof relies on the method of Croot-Lev-Pach and Ellenberg-Gijswijt on the cap set problem, together with a result of Meshulam on linear spaces of low-rank matrices. The result is a modest generalization of the recent bounds on (single-colored and multi-colored) sum-free sets by the author and others.
Publié le : 
@article{DAS_2017_a6,
     author = {Jordan S. Ellenberg},
     title = {Sumsets as unions of sumsets of subsets},
     journal = {Discrete analysis},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2017_a6/}
}
TY  - JOUR
AU  - Jordan S. Ellenberg
TI  - Sumsets as unions of sumsets of subsets
JO  - Discrete analysis
PY  - 2017
UR  - http://geodesic.mathdoc.fr/item/DAS_2017_a6/
LA  - en
ID  - DAS_2017_a6
ER  - 
%0 Journal Article
%A Jordan S. Ellenberg
%T Sumsets as unions of sumsets of subsets
%J Discrete analysis
%D 2017
%U http://geodesic.mathdoc.fr/item/DAS_2017_a6/
%G en
%F DAS_2017_a6
Jordan S. Ellenberg. Sumsets as unions of sumsets of subsets. Discrete analysis (2017). http://geodesic.mathdoc.fr/item/DAS_2017_a6/