Mixed-uniformity product Hilton–Milner conjecture
Let n≥2k>2ℓ≥4n\geq 2k>2\ell\geq 4n≥2k>2ℓ≥4. Fix sets F0∈([2,n]k)F_0\in\binom{[2,n]}{k}F0∈(k[2,n]) and G0∈([2,n]ℓ)G_0\in\binom{[2,n]}{\ell}G0∈(ℓ[2,n]) with F0∩G0≠∅F_0\cap G_0\neq\emptysetF0∩G0=∅, and define … … Two families are cross-intersecting if…