Interval order

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.More formally, a poset $P = (X, leq)$ is an interval order if and only ifthere exists a bijection from $X$ to a set of real intervals,so $x_i mapsto (ell_i, r_i)$ ,such that for any $x_i, x_j in X$ we have $x_i < x_j$ in $P$ exactly when $r_i < ell_j$ .

The complement of the comparability graph of an interval order ( $X$ , ≤)is the interval graph $(X, cap)$ .

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Interval order

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