Separable permutation

In combinatorial mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations may be characterized by the forbidden permutation patterns 2413 and 3142; they are also the permutations whose permutation graphs are cographs and the permutations that realize the series-parallel partial orders. It is possible to test in polynomial time whether a given separable permutation is a pattern in a larger permutation, or to find the longest common subpattern of two separable permutations.