The ranked poset P is Sperner if the maximum size of a rank is the dilworthNumber of P. That is, P is Sperner if the maximum size of a rank is the maximum size of an antichain.
i1 : n = 5; |
i2 : isSperner chain n o2 = true |
i3 : isSperner booleanLattice n o3 = true |
i4 : P = poset {{1,4}, {1,5}, {1,6}, {2,6}, {3,6}}; |
i5 : isSperner P o5 = false |
i6 : isAntichain(P, {2,3,4,5}) o6 = true |
i7 : rankGeneratingFunction P o7 = 3q + 3 o7 : ZZ[q] |