A map from the lower-half of the n-cube onto the (n−1)-cube which preserves intersecting antichains Original Research Article

We prove that there is a 1–1 correspondence between the set of intersecting antichains in the lower-half of the n-cube and the set of intersecting antichains in the (n−1)-cube. This reduces the enumeration of intersecting antichains contained in the former set to that in the latter.