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
-uniform intersecting set
systems over a set of
elements.
Keywords
shifted intersecting set systems, $k$-uniform,
Erdős–Ko–Rado theorem, Hilton–Milner theorem