3 papers
math.CO2026
Interval hypergraphic polytopes (or deformed associahedra), Tamari interval posets, and weeping willows
Jose Bastidas, Félix Gélinas, Vincent Pilaud +3
For a hypergraph on , the hypergraphic polytope is the Minkowski sum of the standard simplices for all .…
math.CO2026
Separating trees and simple congruences of the weak order
Emily Barnard, Jean-Christophe Novelli, Vincent Pilaud
A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in te…
math.CO2025
Geometric realizations of the -weak order and its lattice quotients
Eva Philippe, Vincent Pilaud
For an -tuple of non-negative integers, the -weak order is a lattice structure on -trees, generalizing the weak order on permutations. We first describe the join irred…