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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2001, Volume 35, Issue 3, Pages 36–47 (Mi faa257)

On Polytopes that are Simple at the Edges

V. A. Timorinab

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of Toronto

Abstract: We study some combinatorial properties of polytopes that are simple at the edges. We give an elementary geometric proof of an analog of the hard Lefschetz theorem for the polytopes for which the distance between any two nonsimple vertices is sufficiently large. This implies that the $h$-vector of such polytopes satisfies the relations $h_{[d/2]}\ge h_{[d/2]+1}\ge\cdots\ge h_d=1$, where $d$ is the dimension of the polytope, which proves a special case of Stanley's conjecture.

DOI: https://doi.org/10.4213/faa257

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English version:
Functional Analysis and Its Applications, 2001, 35:3, 189–198

Bibliographic databases:

UDC: 514.172.45+515.165.4

Citation: V. A. Timorin, “On Polytopes that are Simple at the Edges”, Funktsional. Anal. i Prilozhen., 35:3 (2001), 36–47; Funct. Anal. Appl., 35:3 (2001), 189–198

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/faa257
• https://doi.org/10.4213/faa257
• http://mi.mathnet.ru/eng/faa/v35/i3/p36

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This publication is cited in the following articles:
1. Karu, K, “Hard Lefschetz theorem for nonrational polytopes”, Inventiones Mathematicae, 157:2 (2004), 419
2. V. M. Buchstaber, “Ring of Simple Polytopes and Differential Equations”, Proc. Steklov Inst. Math., 263 (2008), 13–37
3. Cattani, E, “Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations”, International Mathematics Research Notices, 2008, rnn025
4. Esterov A., “Characteristic Classes of Affine Varieties and Plucker Formulas For Affine Morphisms”, J. Eur. Math. Soc., 20:1 (2018), 15–59
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