Tensor slice rank and Cayleys first hyperdeterminant
Amanov A. Yeliussizov D.
1 January 2023Elsevier Inc.
Linear Algebra and Its Applications
2023#656224 - 246 pp.
Cayleys first hyperdeterminant is a straightforward generalization of determinants for tensors. We prove that nonzero hyperdeterminants imply lower bounds on some types of tensor ranks. This result applies to the slice rank introduced by Tao and more generally to partition ranks introduced by Naslund. As an application, we show upper bounds on some generalizations of colored sum-free sets based on constraints related to order polytopes.
Hyperdeterminant , Partition rank , Slice rank , Tensors
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Kazakh-British Technical University, Almaty, Kazakhstan
Kazakh-British Technical University
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