Abstract
The central problem among extremal problems in partially ordered sets (posets) is to find the largest set of mutually incomparable elements in a poset. The first results were obtained by Sperner in 1928 [Sr]: the maximum-sized set of mutually incomparable subsets of an n-element set consists of those subsets with [n/2] elements, or those with [n/2] elements. A completely different approach was taken by Dilworth in 1950 [Di]: the size of the largest incomparable collection (antichain) equals the smallest number of totally ordered collections (chains) whose union includes all of the elements of the poset.
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