In additive number theory and combinatorics, a restricted sumset has the form S = { a 1 + ⋯ + a n :   a 1 ∈ A 1 , … , a n ∈ A n   a n d   P ( a 1 , …...

size of A {\displaystyle A} ); see for example Freiman's theorem. Restricted sumset Sidon set Sum-free set Schnirelmann density Shapley–Folkman lemma...

Examples of this type include the Erdős–Heilbronn Conjecture (for a restricted sumset) and the Cauchy–Davenport Theorem. The methods used for tackling such...

topics of Paul Erdős in combinatorial number theory: covering systems, restricted sumsets, and zero-sum problems or EGZ Theorem. With Stephen Redmond, he posed...

Schnirelmann density Shapley–Folkman lemma Sidon set Sum-free set Restricted sumset Sum-product phenomenon Green, Ben (July 2009). "Book Reviews: Additive...

The set of pairwise sums is A + A = {a + b : a,b ∈ A} and is called the sumset of A. The set of pairwise products is A · A = {a · b : a,b ∈ A} and is called...

Typical topics include covering system, zero-sum problems, various restricted sumsets, and arithmetic progressions in a set of integers. Algebraic or analytic...

PlanetMath Erdős, Ginzburg, Ziv Theorem Sun, Zhi-Wei, "Covering Systems, Restricted Sumsets, Zero-sum Problems and their Unification" Zero-sum problems - A survey...

nonempty subsets of the set N {\displaystyle N} of nonnegative integers. The sumset A + B {\displaystyle A+B} is defined by A + B = { a + b : a ∈ A , b ∈ B...

also concerns sumsets in groups but is restricted to groups whose order is a prime number. The first three statements deal with sumsets whose size (in...

problem sorts the sumset, the set of sums of pairs, with duplicate sums condensed to a single value. For this variant, the size of the sumset may be significantly...