Order Dimension
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High Quality Content by WIKIPEDIA articles! In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik Miller dimension of the partial order. Dushnik & Miller (1941) first studied order dimension; for a more detailed treatment of this subject than provided here, see Trotter (1992).Let n be a positive integer, and let P be the partial order on the elements ai and bi (for 1 i n) in which ai bj whenever i j, but no other p...
High Quality Content by WIKIPEDIA articles! In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik Miller dimension of the partial order. Dushnik & Miller (1941) first studied order dimension; for a more detailed treatment of this subject than provided here, see Trotter (1992).Let n be a positive integer, and let P be the partial order on the elements ai and bi (for 1 i n) in which ai bj whenever i j, but no other pairs are comparable. In particular, ai and bi are incomparable in P; P can be viewed as an oriented form of a crown graph. The illustration shows an ordering of this type for n = 4.
