Parallel algorithms for separable permutations

Subclasses of the Separable Permutations

The separable permutations are those that can be obtained from the trivial permutation by two operations called direct sum and skew sum. This class of permutations contains the class of stack sortable permutations,Avp231q, which are enumerated by the Catalan numbers. We prove that all subclasses of the separable permutations which do not contain Avp231q or a symmetry of this class have rational...

Unsplittable Classes of Separable Permutations

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

The Brownian Limit of Separable Permutations

Context of our work. Describing typical properties of permutations in a given class is a question that has received quite a lot of attention in the last few years. Most of the attention is focused on permutation classes Av(τ) for τ of size 3. See for instance the very precise description of the asymptotic shape of permutations in these classes by Miner and Pak [12], or the link between large ra...

Equipopularity Classes in the Separable Permutations

When two patterns occur equally often in a set of permutations, we say that these patterns are equipopular. Using both structural and analytic tools, we classify the equipopular patterns in the set of separable permutations. In particular, we show that the number of equipopularity classes for length n patterns in the separable permutations is equal to the number of partitions of the integer n− 1.

Longest Common Separable Pattern Among Permutations