Stokes posets and serpent nests

Understand

We study two different objects attached to an arbitrary quadrangulation of a regular polygon.

• The first one is a poset, closely related to the Stokes polytopes introduced by Baryshnikov.
• The second one is a set of some paths configurations inside the quadrangulation, satisfying some specific constraints.
• These objects provide a generalisation of the existing combinatorics of cluster algebras and nonnesting partitions of type A.