Year: 2026
Type: preprint
Abstract: 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 face numbers increase weakly along the admissible family of chain--order polytopes when one order coordinate is replaced by a chain coordinate. We also prove that, unless the order and chain polytopes are unimodularly equivalent, all face-number inequalities in dimensions $2,\ldots,|P|-1$ are strict.
Source: arXiv (Cornell University)
Author: Fourier, Ghislain
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214011826