Two-Dimensional Faces of Order and Chain Polytopes

2025/09/22 by Ragnar Freij-Hollanti, Freij-Hollanti, Ragnar, Teemu Lundström +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2509.17541

openalex publication_date 2025/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit combinatorial description of the two-dimensional faces of both the order polytope O(P) and the chain polytope C(P) of a partially ordered set P. Using these descriptions, we show that for any P, C(P) has equally many square faces, and at least as many triangular faces, as O(P) does. Moreover, the inequality is shown to be strict except when O(P) and C(P) are unimodularly equivalent. This proves the case i=2 of a conjecture by Hibi and Li.

Citations

• Gap between the number of facets of the two poset polytopes
• Triangular faces of the order and chain polytope of a maximal ranked poset
• Order and chain polytopes of maximal ranked posets
• A survey of congruences and quotients of partially ordered sets
• The numbers of edges of the order polytope and the chain poyltope of a finite partially ordered set
• Cutting convex polytopes by hyperplanes
• Unimodular equivalence of order and chain polytopes

Cited by

• Simplex inequalities of order and chain polytopes of recursively defined posets

Related

• Triangular faces of the order and chain polytope of a maximal ranked poset
• Simplex inequalities of order and chain polytopes of recursively defined posets
• Simplex faces of order and chain polytopes
• The numbers of edges of the order polytope and the chain poyltope of a finite partially ordered set
• Gap between the number of facets of the two poset polytopes