Right now, we iterate through all planar set partitions in algebras.PlanarPartition by filtering out the non-planar diagrams. However, this is very inefficient for large values of n. We implement a recursive algorithm that works by simply taking the part {a, b, c, ...} that contains the largest element and uses the fact that we can form the planar partition by combining the planar set partitions on the remaining sets {1, ..., a-1}, {a+1, ..., b-1}, ..., which are all independent.

CC: @srdoty @fchapoton @zabrocki @anneschilling @saliola

Component: combinatorics

Keywords: set partition, diagram algebra

Author: Travis Scrimshaw

Branch/Commit: 22d8a70

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/34579