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.

Source : oai:HAL:hal-01147113v4

Volume: Vol. 18 no. 3

Section: Combinatorics

Published on: December 2, 2016

Submitted on: December 2, 2016

Keywords: poset,Tamari lattice,quadrangulation,MSC: 05E 06A11 13F60,[MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA]

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