Remarks on the upper bound theorem.

DOI10.1016/S0097-3165(03)00137-7zbMath1042.52006MaRDI QIDQ1417958

Isabella Novik

Publication date: 6 January 2004

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

zbMATH Keywords

simplicial complexupper bound theoremsimplicial polytopesimplicial manifold\(k\)-neighbourly polytopestrong upper bound theorem

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05)

Related Items (4)

Highly neighborly centrally symmetric spheres ⋮ Relative Stanley-Reisner theory and upper bound theorems for Minkowski sums ⋮ On face numbers of manifolds with symmetry ⋮ Type-B generalized triangulations and determinantal ideals

Cites Work

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• A simple proof of the upper bound theorem
• The number of faces of a simplicial convex polytope
• A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
• The non-neighbourliness of centrally symmetric convex polytopes having many vertices
• A monotonicity property of \(h\)-vectors and \(h^*\)-vectors
• Upper bound theorems for homology manifolds
• A short simplicial \(h\)-vector and the upper bound theorem
• Combinatorics and commutative algebra.
• The Upper Bound Conjecture and Cohen-Macaulay Rings
• On the Number of Vertices of a Convex Polytope
• A Combinatorial Analogue of Poincaré's Duality Theorem
• Diagrams for centrally symmetric polytopes
• The maximum numbers of faces of a convex polytope

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