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math.CO2026
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…
math.CO2026
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…
math.CO2026
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…