Additive combinatorics

The additive structure of sets in integers and abelian groups: sumsets and inverse theorems, sum-product growth, Sidon sets and difference sets, sum-free sets, additive bases, zero-sum problems, and arithmetic progressions in dense sets; colouring (Ramsey-type) versions go to Ramsey theory.

• Sumsets and inverse theorems
• Sets with more sums than differences
• Sidon sets and difference sets
• Sum-free sets
• Additive bases
• Zero-sum problems and subset sums
• Arithmetic progressions in dense sets

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