Sum-free sets in abelian groups
Sum-free sets in abelian groups
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阿贝尔群中的无和集
DOI：
10.1007/bf02773386
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发表时间：
2001
影响因子：
1
通讯作者：
T. Schoen
中科院分区：
文献类型：
--
作者：
V. Lev;Tomasz Łuczak;T. Schoen
证明了存在一个绝对常数δ>；0，使得任意有限交换群G的无和子集的个数为
$$\Left({2^{\nu(G)}-1}\Right)2^{\Left|G\Right|/2}+O\Left({2^{(1/2-\Delta)\Left|G\Right|}\Right)$$
其中ν(G)是G的标准分解为其循环子群的直和的偶数阶分量的个数，且其符号中的隐常数是绝对的。
AbstractWe show that there is an absolute constant δ>0 such that the number of sum-free subsets of any finite abelian groupG is
$$\left( {2^{\nu (G)} - 1} \right)2^{\left| G \right|/2} + O\left( {2^{(1/2 - \delta )\left| G \right|} } \right)$$
whereν(G) is the number of even order components in the canonical decomposition ofG into a direct sum of its cyclic subgroups, and the implicit constant in theO-sign is absolute.