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The partition rank of a tensor and k-right corners in Fqn
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2020-03-17 , DOI: 10.1016/j.jcta.2019.105190
Eric Naslund

Following the breakthrough of Croot, Lev, and Pach [4], Tao [10] introduced a symmetrized version of their argument, which is now known as the slice rank method. In this paper, we introduce a more general version of the slice rank of a tensor, which we call the Partition Rank. This allows us to extend the slice rank method to problems that require the variables to be distinct. Using the partition rank, we generalize a recent result of Ge and Shangguan [6], and prove that any set AFqn of size|A|>(n+(k1)q(k1)(q1)) contains a k-right-corner, that is distinct vectors x1,,xk,xk+1 where x1xk+1,,xkxk+1 are mutually orthogonal, for q=pr, a prime power with p>k.



中文翻译:

张量的划分等级和k的右角Fqñ

随着Croot,Lev和Pach [4]的突破,Tao [10]引入了他们的参数的对称形式,现在称为切片秩方法。在本文中,我们介绍了张量的切片等级的更一般的版本,我们称之为分区等级。这使我们可以将切片等级方法扩展到要求变量不同的问题。利用划分等级,我们推广了葛和上官[6]的最新结果,并证明了任何集一种Fqñ 大小|一种|>ñ+ķ-1个qķ-1个q-1个包含k-right-corner,这是不同的向量X1个XķXķ+1个 哪里 X1个-Xķ+1个Xķ-Xķ+1个 互相正交 q=p[R,具有 p>ķ

更新日期:2020-03-17
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