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Posets :: isStrictSperner

isStrictSperner -- determines if a ranked poset has the strict Sperner property

Synopsis

Description

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

See also

Ways to use isStrictSperner :