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within it is larger than the largest rank level (one of the sets of elements of the same rank) in the poset. Since every rank level is itself an antichain, the
Sperner property is equivalently the property that some rank level is a maximum antichain. The Sperner property and Sperner posets are named
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of a finite set (partially ordered by set inclusion) has this property. The lattice of partitions of a finite set typically lacks the
Sperner property.
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Handbook of discrete and combinatorial mathematics, by
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is a graded poset in which all maximum antichains are rank levels.
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largest rank levels, or, equivalently, the poset has a maximum
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