Order and chain polytopes of maximal ranked posets

2023/09/04 by Ahmad, Ibrahim, Fourier, Ghislain, Joswig, Michael · 2 citations
#52B05 #52B20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.01626

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.

Cited by

• Simplex inequalities of order and chain polytopes of recursively defined posets
• Two-Dimensional Faces of Order and Chain Polytopes

Related

• Triangular faces of the order and chain polytope of a maximal ranked poset
• Signed Poset Polytopes
• Order polytopes of graded posets are gamma-effective
• Order Polytopes of Dimension ≤ 13 are Ehrhart Positive
• 2-levelness of Marked Poset Polytopes and the Ehrhart polynomial