We review facts about rank, multilinear rank, multiplex rank and generic rank of tensors as well as folding of a tensor into a matrix of multihomogeneous polynomials. We define the new concept of folding rank of tensors and compare its properties to other ranks. We review the concept of determinantal schemes associated to a tensor. Then we define the new concept of a folding generic tensor meaning that all its determinantal schemes behave generically. Our main theorem states that for ``small'' 3-tensors, any folding generic tensor has generic rank, and the reverse does not always hold.
"Polynomial foldings and rank of tensors." J. Commut. Algebra 8 (2) 173 - 206, 2016. https://doi.org/10.1216/JCA-2016-8-2-173