Characterizing maximal shifted intersecting set systems and short injective proofs of the Erdős–Ko–Rado and Hilton–Milner theorems

Abstract

We give a canonical partition of shifted intersecting set systems, from which one can obtain unified and elementary proofs of the Erdős–Ko–Rado and Hilton–Milner theorems, as well as a characterization of maximal shifted k-uniform intersecting set systems over a set of n elements.