**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Sumset

Summary

In additive combinatorics, the sumset (also called the Minkowski sum) of two subsets A and B of an abelian group G (written additively) is defined to be the set of all sums of an element from A with an element from B. That is,
:A + B = {a+b : a \in A, b \in B}.
The n-fold iterated sumset of A is
:nA = A + \cdots + A,
where there are n summands.
Many of the questions and results of additive combinatorics and additive number theory can be phrased in terms of sumsets. For example, Lagrange's four-square theorem can be written succinctly in the form
:4,\Box = \mathbb{N},
where \Box is the set of square numbers. A subject that has received a fair amount of study is that of sets with small doubling, where the size of the set A+A is small (compared to the size of A); see for example Freiman's theorem.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related courses

Related lectures

No results

No results

Related publications

Related people

No results

No results

Related units

No results

Related concepts

No results