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About: Interval order     Goto   Sponge   NotDistinct   Permalink

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In mathematics, especially order theory,the interval order for a collection of intervals on the real lineis the partial order corresponding to their left-to-right precedence relation—one interval, I1, being considered less than another, I2, if I1 is completely to the left of I2.More formally, a countable poset is an interval order if and only ifthere exists a bijection from to a set of real intervals,so ,such that for any we have in exactly when .Such posets may be equivalentlycharacterized as those with no induced subposet isomorphic to thepair of two-element chains, in other words as the -free posets.