Polynomial bound for the partition rank vs the analytic rank of tensors

@article{Janzer2019PolynomialBF,
  title={Polynomial bound for the partition rank vs the analytic rank of tensors},
  author={O. Janzer},
  journal={arXiv: Combinatorics},
  year={2019}
}
  • O. Janzer
  • Published 2019
  • Mathematics
  • arXiv: Combinatorics
A tensor defined over a finite field $\mathbb{F}$ has low analytic rank if the distribution of its values differs significantly from the uniform distribution. An order $d$ tensor has partition rank 1 if it can be written as a product of two tensors of order less than $d$, and it has partition rank at most $k$ if it can be written as a sum of $k$ tensors of partition rank 1. In this paper, we prove that if the analytic rank of an order $d$ tensor is at most $r$, then its partition rank is at… Expand
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