Tensor Rank: Some Lower and Upper Bounds

@article{Alexeev2011TensorRS,
  title={Tensor Rank: Some Lower and Upper Bounds},
  author={B. Alexeev and Michael A. Forbes and Jacob Tsimerman},
  journal={2011 IEEE 26th Annual Conference on Computational Complexity},
  year={2011},
  pages={283-291}
}
  • B. Alexeev, Michael A. Forbes, Jacob Tsimerman
  • Published 2011
  • Computer Science, Mathematics
  • 2011 IEEE 26th Annual Conference on Computational Complexity
  • The results of Strassen~\cite{strassen-tensor} and Raz~\cite{raz} show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we construct field-independent explicit 0/1 tensors T:[n]^d\to\mathbb{F} with rank at least 2n^{\lfloor d/2\rfloor}+n-\Theta(d\lg n). This improves the lower-order terms in known lower bounds for any odd d\ge 3. We also explore a… CONTINUE READING
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