Stephen B. Maurer

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The rank (resp. dimension) of a poset P is the cardinality of a largest (resp. smallest) set of linear orders such that its intersection is P and no proper subset has intersectior: P. Dimension has been studied extensively. Rank was introduced recently by Maurer and Rabinovitch in [4], where the rank of antichains was determined. In this paper we develop a(More)
We consider An extremal problem for directed graphs which is closely related to Tutin's theorem giving the maximum number of edges in a gr;lph on n vertices which does not contain a complete subgraph on m vertices. and edge set {(i. j): 1 s i C j s n]. A subgraph H of T,, is said to be m-locally unipathic when the restriction of H to each m element subset(More)
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