Tensor surgery and tensor rank

@article{Christandl2018TensorSA,
  title={Tensor surgery and tensor rank},
  author={Matthias Christandl and Jeroen Zuiddam},
  journal={computational complexity},
  year={2018},
  volume={28},
  pages={27-56}
}
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices and edges. We show that tensor surgery is capable of preserving the low rank structure of an initial tensor decomposition and thus allows to prove nontrivial upper bounds on tensor rank, border rank and… 
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