Resumen de Multitriangulations and tropical Pfaffians

Luis Crespo Ruiz, Francisco Santos

• The k-asociahedron is a simplicial complex whose facets correspond to k-triangulationsof the n-gon, known to be homeomorphic to a sphere of dimension k(n − 2k − 1) − 1 andconjectured to be polytopal by Jonsson, among others. (The case or k = 1 is the classicalassociahedron of dimension n − 4). We show that it can be obtained by intersecting thetropical variety of Pfaffians with the orthant of “four-point positive” weights. We hope thisto be a step towards realizing it as a polytope.