We study tensors in Cm×n×l whose border rank is l. We give a set-theoretic char-
acterization of tensors in C3×3×4 and in C4×4×4 of border rank 4 at most.
Publisher StatementNOTICE: this is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, [June 23, 2011] DOI:10.1016/j.laa.2011.05.013.
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