An Improvement on Ranks of Explicit Tensors

Abstract

We give constructions of n × n × n tensors of rank at least 2n − O(n). As a corollary we obtain an [n] shaped tensor with rank at least 2n − O(n) 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… (More)

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