# 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}
}
• 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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