It is shown that if V ⊆ ${F}_{p}^{n}$ ×⋯×np is a subspace of d-tensors with dimension at least tnd-1, then there is a subspace W ⊆ V of dimension at least t/(dr)−1 p is a subspace of d-tensors with dimension whose nonzero elements all have analytic rank Ωd,p(r). As an application, we generalize a result of Altman on Szemerédi's theorem with random differences.
Online Journal of Analytic Combinatorics
Networks
Algorithms and Complexity

Briët, J. (2019). Subspaces of tensors with high analytic rank. Online Journal of Analytic Combinatorics, 6(16).