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.
Alexander Garver;Thomas McConville, 2020, Oriented Flip Graphs and Noncrossing Tree Partitions, Discrete mathematics and theoretical computer science/Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th..., 10.46298/dmtcs.6379, https://doi.org/10.46298/dmtcs.6379.
Song He;Zhenjie Li;Prashanth Raman;Chi Zhang, 2020, Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra, The Journal of high energy physics/The journal of high energy physics, 2020, 10, 10.1007/jhep10(2020)054, https://doi.org/10.1007/jhep10(2020)054.
Thibault Manneville;Vincent Pilaud, 2018, Geometric Realizations of the Accordion Complex of a Dissection, Discrete and computational geometry/Discrete & computational geometry, 61, 3, pp. 507-540, 10.1007/s00454-018-0004-2, https://doi.org/10.1007/s00454-018-0004-2.