# 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
A note on extensions of multilinear maps defined on multilinear varieties
• Mathematics
• Proceedings of the Edinburgh Mathematical Society
• 2021
An Optimal Inverse Theorem
• Computer Science, Mathematics
• ArXiv
• 2021
Structure vs. randomness for bilinear maps
• Computer Science, Mathematics
• STOC
• 2021

#### References

SHOWING 1-10 OF 19 REFERENCES
The partition rank of a tensor and k-right corners in Fqn
• E. Naslund
• Mathematics, Computer Science
• J. Comb. Theory, Ser. A
• 2020
The distribution of polynomials over finite fields, with applications to the Gowers norms
• Mathematics, Computer Science
• Contributions Discret. Math.
• 2009
Subsets of Cayley Graphs that Induce Many Edges
• Computer Science, Mathematics
• Theory Comput.
• 2019