In
mathematics, especially
order theory, the
interval order for a collection of intervals on the real line is 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
poset is an interval order if and only if there exists a bijection from
to a set of real intervals, so
, such that for any
we have
in
exactly when
. Such posets may be equivalently characterized as those with no induced subposet isomorphic to the pair of two element chains, the free posets .