Equality in the LYM inequality
= Equality in the LYM inequality
An <antichain> in the <Boolean lattice> has <Lubell mass> one if and only if it is a full rank level. Equality means every <maximal chain in a Boolean lattice> meets the family exactly once. Swapping two adjacent entries in the defining <permutation> then forces the family to contain every set obtained from one member by exchanging an included and an excluded element, hence every set of that rank.