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

Lev, Vsevolod F.

Period. Math. Hung. 42, No. 1-2, 89-98 (2001).

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