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

Keywords:

restricted sumset

Citations:

Zbl 0964.11016; Zbl 0973.11026
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