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Mathematics | Vol.7, Issue.9 | | Pages

Faces of 2-Dimensional Simplex of Order and Chain Polytopes

Aki Mori

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.

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Faces of 2-Dimensional Simplex of Order and Chain Polytopes

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Keywords

faces of 2dimensional simplex facets of the order and chain polytope 2faces vertices edges order

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Aki Mori,.Faces of 2-Dimensional Simplex of Order and Chain Polytopes. 7 (9),.

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