\(f\)-vectors of barycentric subdivisions

DOI10.1007/s00209-007-0251-zzbMath1158.52013arXivmath/0606356OpenAlexW2086949194MaRDI QIDQ930501

Francesco Brenti, Volkmar Welker

Publication date: 30 June 2008

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606356

zbMATH Keywords

\(f\)-vector\(h\)-vectorbarycentric subdivision

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20)

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Cites Work

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• Complexes of injective words and their commutation classes
• Some aspects of groups acting on finite posets
• \(q\)-Eulerian polynomials arising from Coxeter groups
• Flag \(f\)-vectors and the \(cd\)-index
• On the Charney-Davis and Neggers-Stanley conjectures
• Chain polynomials of distributive lattices are 75\% unimodal
• The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold
• Real root conjecture fails for five- and higher-dimensional spheres
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• Matrix Analysis
• On linear transformations preserving the Pólya frequency property
• The cd-index of fans and posets