The number of additive triples in subsets of abelian groups
The number of additive triples in subsets of abelian groups
复制标题
阿贝尔群子集中的加法三元组的数量
DOI：
10.1017/s0305004115000821
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发表时间：
2015
影响因子：
0.8
通讯作者：
B. Sudakov
中科院分区：
文献类型：
--
作者：
Wojciech Samotij;B. Sudakov
有限阿贝尔群的一组元素如果不包含Schur三元组，即不包含x + y = z的元素x， y， z的三元组，则称为无和。给定阿贝尔群的最大无和子集有多大的研究已经开始了三十多年，直到十年前才由Green和Ruzsa最终解决。我们解决以下更普遍的问题。假设一个由阿贝尔群G的元素组成的集合a具有基数a。a必须包含多少个舒尔三元组？此外，G的a个元素的哪个集合有最少的舒尔三元组？在本文中，我们对各种群G和a的值域回答了这些问题。
Abstract 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 x, y, z with x + y = z. 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 A of elements of an abelian group G has cardinality a. How many Schur triples must A contain? Moreover, which sets of a elements of G have the smallest number of Schur triples? In this paper, we answer these questions for various groups G and ranges of a.
排列中长度为 4 的单调子序列的最小数量
DOI：
10.1017/s0963548314000820
发表时间：
2014
期刊：
Combinatorics, Probability and Computing
影响因子：
--
作者：
BALOGH J
通讯作者：
BALOGH J