置换的遗传性质是强可检验的
Hereditary properties of permutations are strongly testable
摘要：
我们证明了对于每一个遗传置换性质P和eps>0，存在一个整数M，使得如果置换p在Kendall τ距离中eps-远于P，则p的M阶随机子置换具有概率至多eps的性质P.这解决了一个公开的问题，即遗传置换性质是否是强可测试的，即，Kendall’s tau距离的相关性此外，我们的方法也产生了一个猜想的证明Hoppen，Kohayakawa，Moreira和Sampaio的矩形距离和Kendall的tau距离的关系的一个置换从遗传性质。
英文摘要：
We show that for every hereditary permutation property P and every eps>0, there exists an integer M such that if a permutation p is eps-far from P in the Kendall's tau distance, then a random subpermutation of p of order M has the property P with probability at most eps. This settles an open problem whether hereditary permutation properties are strongly testable, i.e., testable with respect to the Kendall's tau distance. In addition, our method also yields a proof of a conjecture of Hoppen, Kohayakawa, Moreira and Sampaio on the relation of the rectangular distance and the Kendall's tau distance of a permutation from a hereditary property.
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