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Restricted set addition in groups. III: Integer sumsets with generic restrictions. (English) Zbl 1012.11020

Summary: Let \(A\) be a finite set of integers. Assuming that \(\mathcal R\subseteq A\times A\) is not “too large”, we give a lower-bound estimate for the cardinality of the restricted sumset \[ A\overset{\mathcal R} + A:=\{a_1+a_2:a_1,a_2\in A,\;(a_1,a_2)\not\in \mathcal R\} \] in terms of the cardinality and the length of \(A\).
For Parts I and II, see Zbl 0964.11016 and Zbl 0973.11026.

MSC:

11B75 Other combinatorial number theory
11P99 Additive number theory; partitions
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C35 Extremal problems in graph theory
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