Order and chain polytopes of maximal ranked posets
arXiv:2309.01626 · doi:10.1016/j.dam.2026.03.036
Abstract
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 Nan Li states that the -vector of the chain polytope dominates the -vector of the order polytope. In this paper we prove a stronger form of that conjecture for a special class of posets. More precisely, we show that the -vectors increase monotonically over an admissible family of chain-order polytopes for such posets.
16 pages