1 research outputs found
The number of additive triples in subsets of abelian groups
A set of elements of a finite abelian group is called sum-free if it contains
no Schur triple, i.e., no triple of elements with . The study of
how large the largest sum-free subset of a given abelian group is had started
more than thirty years before it was finally resolved by Green and Ruzsa a
decade ago. We address the following more general question. Suppose that a set
of elements of an abelian group has cardinality . How many Schur
triples must contain? Moreover, which sets of elements of have the
smallest number of Schur triples? In this paper, we answer these questions for
various groups and ranges of .Comment: 20 pages; corrected the erroneous equality in (1) in the statement of
Theorem 1.