TY - JOUR
T1 - On the structure of sum-free sets, 2
AU - Deshouillers, Jean Marc
AU - Freiman, Gregory A.
AU - Sós, Vera
AU - Temkin, Mikhail
PY - 1999
Y1 - 1999
N2 - A finite set of positive integers is called sum-free if double-struck A∩n (double-struck A + double-struck A) is empty, where double-struck A + double-struck A denotes the set of sums of pairs of non necessarily distinct elements from double-struck A. Improving upon a previous result by G.A. Freiman, a precise description of the structure of sum-free sets included in [1, M] with cardinality larger than 0.4M - x for M ≥ M0(x) (where x is an arbitrary given number) is given.
AB - A finite set of positive integers is called sum-free if double-struck A∩n (double-struck A + double-struck A) is empty, where double-struck A + double-struck A denotes the set of sums of pairs of non necessarily distinct elements from double-struck A. Improving upon a previous result by G.A. Freiman, a precise description of the structure of sum-free sets included in [1, M] with cardinality larger than 0.4M - x for M ≥ M0(x) (where x is an arbitrary given number) is given.
KW - Additive number theory
KW - Arithmetic progressions
KW - Combinatorial number theory
KW - Sum-free sets
UR - http://www.scopus.com/inward/record.url?scp=0001171386&partnerID=8YFLogxK
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AN - SCOPUS:0001171386
SN - 0303-1179
VL - 258
SP - 149
EP - 161
JO - Asterisque
JF - Asterisque
ER -