A proof of Grünbaum's lower bound conjecture for general polytopes

DOI10.1007/s11856-021-2234-xzbMath1493.52013arXiv2004.08429OpenAlexW3215391902WikidataQ113899781 ScholiaQ113899781MaRDI QIDQ2130528

Lei Xue

Publication date: 25 April 2022

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.08429

zbMATH Keywords

polytopeslower bound theoremf-vector

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

The Lower Bound Theorem for $d$-Polytopes with $2{d}+1$ Vertices ⋮ Minimum number of edges of polytopes with \(2d+2\) vertices ⋮ Embedding divisor and semi-prime testability in \(f\)-vectors of polytopes

Cites Work

• The number of faces of a simplicial convex polytope
• Graph theorems for manifolds
• Lower bound theorems for general polytopes
• The minimum number of vertices of a simple polytope
• A proof of the lower bound conjecture for convex polytopes
• Sufficiency of McMullen’s conditions for 𝑓-vectors of simplicial polytopes
• Lectures on Polytopes
• Convex Polytopes
• Convex Polytopes
• The maximum numbers of faces of a convex polytope

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