论文信息 - Large minimal realizers of a partial order II

Large minimal realizers of a partial order II

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 intersection 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 general theory of rank. The main result, loosely stated, is that to each poset P there corresponds a class of graphs with easily described properties, and that the rank of P is the maximum number of edges in a graph in this class.

William T. Trotter | Stephen B. Maurer | I. Rabinovitch

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