显式张量秩的一个改进

摘要：

给出了秩至少为2n^k - O（n^（k-1））的n^k x n^k x n张量的构造.作为推论，当r为奇数时，我们得到了秩至少为2n^（r/2）- O（n^（r/2）-1）的[n]^r形张量.张量构造从一个简单的递归模式，和下界证明使用划分定理开发的Brockett和Dobkin。这两个界是对之前最著名的显式张量的改进，显式张量的秩分别为n^k和n^（r/2

英文摘要：

We give constructions of n^k x n^k x n tensors of rank at least 2n^k - O(n^(k-1)). As a corollary we obtain an [n]^r shaped tensor with rank at least 2n^(r/2) - O(n^(r/2)-1) when r is odd. The tensors are constructed from a simple recursive pattern, and the lower bounds are proven using a partitioning theorem developed by Brockett and Dobkin. These two bounds are improvements over the previous best-known explicit tensors that had ranks n^k and n^(r/2) respectively

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