Order Dimension
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 DushnikâMiller 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).
Read more about Order Dimension: Formal Definition, Realizers, Example, Order Dimension Two, Computational Complexity, Incidence Posets of Graphs, K-dimension and 2-dimension
Famous quotes containing the words order and/or dimension:
“Judicial judgment must take deep account ... of the day before yesterday in order that yesterday may not paralyze today.”
—Felix Frankfurter (18821965)
“By intervening in the Vietnamese struggle the United States was attempting to fit its global strategies into a world of hillocks and hamlets, to reduce its majestic concerns for the containment of communism and the security of the Free World to a dimension where governments rose and fell as a result of arguments between two colonels wives.”
—Frances Fitzgerald (b. 1940)