Larger Corner-Free Sets from Combinatorial Degenerations
summary
Introduces a combinatorial degeneration method that views corner problems as independent sets in a 3-uniform hypergraph power and uses adjacency tensors to guarantee identity blocks on uniform tuples. A small linear program finds a base subset S with three vertex-labeling maps, then tensoring S^n yields large corner-free sets. Claims improve known lower bounds for grid/field cases — notably R(F3^n) grows like at least 3.39^n and a separate construction reaches roughly 7^n — and directly tightens NOF communication upper bounds for the Eval function.
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