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A note on the gap between rank and border rank

Fri, 2015-05-15 17:01 - Jeroen Zuiddam
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Date: 
2015-04-21
Author(s): 

Jeroen Zuiddam

Reference: 

arXiv:1504.05597 [math.AC]

URL: 

http://arxiv.org/abs/1504.05597

We study the tensor rank of a certain algebra. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a counterexample to a conjecture of Rhodes. We also obtain a new lower bound on the tensor rank of powers of the generalized W-state.