Faces of 2-Dimensional Simplex of Order and Chain Polytopes

Aki Mori
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Aki Mori: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan

Mathematics, 2019, vol. 7, issue 9, 1-6

Abstract: 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.

Keywords: order polytope; chain polytope; partially ordered set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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