75 citations · 305 across the 41 of their papers we have counts for
10 papers · 1 filter
The Hibi-Li Face-Number Conjecture
Ghislain Fourier
We prove the face-number conjecture of Hibi and Li: for every finite poset, the order polytope has no more faces of any given dimension than the chain polytope. More generally, the…
Makhlin polytopes are Demazure string polytopes
Ghislain Fourier
We show that Makhlin's polytopes in type are unimodularly equivalent to string polytopes for Demazure modules in type . The proof passes through type , combining…
On facet gaps of order and chain polytopes
Ghislain Fourier
We discuss three questions from a recent paper of Bhandari, Cunningham, Morrell, Oh and Smith. We obtain an exact local formula for the facet gap between the order and the chain po…
Order and chain polytopes of maximal ranked posets
Ibrahim Ahmad, Ghislain Fourier, Michael Joswig
The order and chain polytopes, introduced by Richard P. Stanley, form a pair of Ehrhart equivalent polytopes associated to a given finite poset. A conjecture by Takayuki Hibi and N…
The Minkowski Property and Reflexivity of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Christoph Pegel
We provide a Minkowski sum decomposition of marked chain-order polytopes into building blocks associated to elementary markings and thus give an explicit minimal set of generators…
Symmetries on plabic graphs and associated polytopes
Xin Fang, Ghislain Fourier
For Grassmann varieties, we explain how the duality between the Gelfand-Tsetlin polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes arises from different positive structu…