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- Q8348314 subject Q13287074.
- Q8348314 abstract "Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.Research in polyhedral combinatorics falls into two distinct areas. Mathematicians in this area study the combinatorics of polytopes; for instance, they seek inequalities that describe the relations between the numbers of vertices, edges, and faces of higher dimensions in arbitrary polytopes or in certain important subclasses of polytopes, and study other combinatorial properties of polytopes such as their connectivity and diameter (number of steps needed to reach any vertex from any other vertex). Additionally, many computer scientists use the phrase “polyhedral combinatorics” to describe research into precise descriptions of the faces of certain specific polytopes (especially 0-1 polytopes, whose vertices are subsets of a hypercube) arising from integer programming problems.".
- Q8348314 thumbnail Pyramid_face_lattice.svg?width=300.
- Q8348314 wikiPageExternalLink five-open-problems-regarding-convex-polytopes.
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- Q8348314 comment "Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.Research in polyhedral combinatorics falls into two distinct areas.".
- Q8348314 label "Polyhedral combinatorics".
- Q8348314 depiction Pyramid_face_lattice.svg.
