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arXiv · 2309.01626

Order and chain polytopes of maximal ranked posets

Ibrahim Ahmad·Ghislain Fourier·Michael Joswig
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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 $f$-vector of the chain polytope dominates the $f$-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 $f$-vectors increase monotonically over an admissible family of chain-order polytopes for such posets.

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Ibrahim Ahmad, Ghislain Fourier, Michael Joswig. 2025-01-29. Order and chain polytopes of maximal ranked posets. https://doi.org/10.1016/j.dam.2026.03.036

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