Simplex Inequalities of Order and Chain Polytopes of Recursively Defined Posets
Abstract
Abstract In this paper, we study the simplex faces of the order polytope $$\mathcal {O}(P)$$ O ( P ) and the chain polytope $$\mathcal {C}(P)$$ C ( P ) of a finite poset P . We show that, if P can be recursively constructed from $$\textbf{X}$$ X -free posets using disjoint unions and ordinal sums, then $$\mathcal {C}(P)$$ C ( P ) has at least as many k -dimensional simplex faces as $$\mathcal {O}(P)$$ O ( P ) does, for each dimension k . This generalizes a previous result of Mori, both in terms of the dimensions of the simplices and in terms of the class of posets considered.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Graph Theory Research
Point processes and geometric inequalities
Publication details
- Journal / source
- Order
- Volume
- 43
- Issue
- 3
- Publication date
- 2 September 2026
- Language
- EN