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

This article is cited in 4 scientific papers (total in 4 papers)

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

Full text: PDF file (188 kB)
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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
Received: 05.06.2000

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. V. M. Buchstaber, “Ring of Simple Polytopes and Differential Equations”, Proc. Steklov Inst. Math., 263 (2008), 13–37  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. Cattani, E, “Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations”, International Mathematics Research Notices, 2008, rnn025  crossref  mathscinet  zmath  isi  scopus
    4. Esterov A., “Characteristic Classes of Affine Varieties and Plucker Formulas For Affine Morphisms”, J. Eur. Math. Soc., 20:1 (2018), 15–59  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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