The ranked poset P is strict Sperner if the maximalAntichains are the sets of elements with the same rank.
The n chain is strict Sperner as the maximal antichains and the sets of elements with the same rank are singletons.
i1 : isStrictSperner chain 5 o1 = true |
The n booleanLattice, for n ≥3, is not strict Sperner as it has maximal antichains which are not sets of elements with the same rank.
i2 : B = booleanLattice 3; |
i3 : isStrictSperner B o3 = false |
i4 : rankPoset B o4 = {{000}, {001, 010, 100}, {011, 101, 110}, {111}} o4 : List |
i5 : maximalAntichains B o5 = {{000}, {111}, {001, 110}, {010, 101}, {011, 100}, {001, 010, 100}, {011, 101, 110}} o5 : List |