For cross t-intersecting families of k- and l-dimensional subspaces with no common t-subspace, the product-maximizing pairs are exactly three explicit families A, H, and C.
Tokushige, The eigenvalue method for crosst-intersecting families,J
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Extremal cross $t$-intersecting families under $t$-covering number constraints for vector spaces
For cross t-intersecting families of k- and l-dimensional subspaces with no common t-subspace, the product-maximizing pairs are exactly three explicit families A, H, and C.