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1 Introduction An antichain in a poset is a collection of pairwise incomparable elements of , and the width of , denoted by , is the size of the largest antichain in . The Boolean lattice is the poset consisting of all subsets of partially ordered by containment. The Boolean lattice is naturally partitioned into antichains which we call the layers of the Boolean lattice, denoted by for , which are all subsets of of size .
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