Interval Order

A partially ordered set P=(X,<=) is an interval order if it is isomorphic to some set of intervals on the real line ordered by left-to-right precedence. Formally, P is an interval order provided that one can assign to each x in X an interval [x_L,x_R] such that x_R<y_L in the real numbers iff x<y in P.

See also

Partially Ordered Set

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Fishburn, P. C. Interval Orders and Interval Graphs: A Study of Partially Ordered Sets. New York: Wiley, 1985.Wiener, N. "A Contribution to the Theory of Relative Position." Proc. Cambridge Philos. Soc. 17, 441-449, 1914.

Referenced on Wolfram|Alpha

Interval Order

Cite this as:

Weisstein, Eric W. "Interval Order." From MathWorld--A Wolfram Web Resource.

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