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Posets :: isAntichain

isAntichain -- checks whether a subposet is an anti-chain

Synopsis

Description

This function determines whether a list of elements of a poset is an anti-chain.

i1 : P2 = poset({a,b,c,d,e,f,g}, {(a,b), (a,c), (a,d), (b,e), (c,e), (c,f), (d,f), (e,g), (f,g)})

o1 = Poset{cache => CacheTable{}                                                                }
           GroundSet => {a, b, c, d, e, f, g}
           RelationMatrix => | 1 1 1 1 1 1 1 |
                             | 0 1 0 0 1 0 1 |
                             | 0 0 1 0 1 1 1 |
                             | 0 0 0 1 0 1 1 |
                             | 0 0 0 0 1 0 1 |
                             | 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 1 |
           Relations => {(a, b), (a, c), (a, d), (b, e), (c, e), (c, f), (d, f), (e, g), (f, g)}

o1 : Poset
i2 : isAntichain(P2, {a,b})

o2 = false
i3 : isAntichain(P2, {b,c,d})

o3 = true

Ways to use isAntichain :

  • isAntichain(Poset,List)