**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# Restricted sumset

Summary

In additive number theory and combinatorics, a restricted sumset has the form
:S={a_1+\cdots+a_n:\ a_1\in A_1,\ldots,a_n\in A_n \ \mathrm{and}\ P(a_1,\ldots,a_n)\not=0},
where A_1,\ldots,A_n are finite nonempty subsets of a field F and P(x_1,\ldots,x_n) is a polynomial over F.
If P is a constant non-zero function, for example P(x_1,\ldots,x_n)=1 for any x_1,\ldots,x_n, then S is the usual sumset A_1+\cdots+A_n which is denoted by nA if A_1=\cdots=A_n=A.
When
:P(x_1,\ldots,x_n) = \prod_{1 \le i < j \le n} (x_j-x_i),
S is written as A_1\dotplus\cdots\dotplus A_n which is denoted by n^{\wedge} A if A_1=\cdots=A_n=A.
Note that |S| > 0 if and only if there exist a_1\in A_1,\ldots,a_n\in A_n with P(a_1,\ldots,a_n)\not=0.
Cauchy–Davenport theorem
The Cauchy–Daven

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 people

Related publications

Related units

No results

No results

No results

Related lectures

Related concepts

Related courses

No results

No results

No results