On subsets of abelian groups with no 3-term arithmetic progression
نویسندگان
چکیده
منابع مشابه
On subsets of abelian groups with no 3-term arithmetic progression
A short proof of the following result of Brown and Buhler is given: For any E > 0 there exists n, = no(E) such that if A is an abelian group of odd order IAl > no and BG A with IBI >&IAI. then B must contain three distinct elements X, y, z satisfying x + y = 22.
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Addressing a question of Cameron and Erdős, we show that, for infinitely many values of n, the number of subsets of {1, 2, . . . , n} that do not contain a k-term arithmetic progression is at most 2O(rk(n)), where rk(n) is the maximum cardinality of a subset of {1, 2, . . . , n} without a k-term arithmetic progression. This bound is optimal up to a constant factor in the exponent. For all value...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1987
ISSN: 0097-3165
DOI: 10.1016/0097-3165(87)90053-7