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Open AccessFeature PaperArticle

Faces of 2-Dimensional Simplex of Order and Chain Polytopes

Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
Mathematics 2019, 7(9), 851; https://doi.org/10.3390/math7090851
Received: 11 August 2019 / Revised: 9 September 2019 / Accepted: 10 September 2019 / Published: 14 September 2019
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it will be proved that an arbitrary triangle in 1-skeleton of the order or chain polytope forms the face of 2-dimensional simplex of each polytope. These results mean a generalization in the case of 2-faces of the characterization known in the case of edges. View Full-Text
Keywords: order polytope; chain polytope; partially ordered set order polytope; chain polytope; partially ordered set
MDPI and ACS Style

Mori, A. Faces of 2-Dimensional Simplex of Order and Chain Polytopes. Mathematics 2019, 7, 851.

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