Triangular slice-rank method and set-intersection problems

Extending the slice-rank method for diagonal tensors to triangular tensors, we give new and shorter proofs for some well-known theorems on set-intersections like Frankl-Wilson and Snevily with modular constraints, and some of the more recent set-intersection results. We also improve Snevily with modular constraints in some special cases. Then, using Snevily's theorem with some combinatorial lemmas, we give new bounds on some generalizations of the reverse odd-town problem.