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Uspekhi Mat. Nauk, 2011, Volume 66, Issue 2(398), Pages 67–162 (Mi umn9421)  

This article is cited in 5 scientific papers (total in 6 papers)

Polytopes, Fibonacci numbers, Hopf algebras, and quasi-symmetric functions

V. M. Buchstabera, N. Yu. Erokhovetsb

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

Abstract: This survey is devoted to the classical problem of flag numbers of convex polytopes, and contains an exposition of results obtained on the basis of connections between the theory of convex polytopes and a number of modern directions of research.
Bibliography: 62 titles.

Keywords: flag numbers, flag polynomials, Leibniz–Hopf algebra, Lyndon words, Dehn–Sommerville relations, universal $G$-polynomial, $\boldsymbol{cd}$-index.

DOI: https://doi.org/10.4213/rm9421

Full text: PDF file (1358 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2011, 66:2, 271–367

Bibliographic databases:

UDC: 515.164.8
MSC: Primary 52-02; Secondary 05E05, 06A07, 16T05, 16E45, 52B05
Received: 01.03.2011

Citation: V. M. Buchstaber, N. Yu. Erokhovets, “Polytopes, Fibonacci numbers, Hopf algebras, and quasi-symmetric functions”, Uspekhi Mat. Nauk, 66:2(398) (2011), 67–162; Russian Math. Surveys, 66:2 (2011), 271–367

Citation in format AMSBIB
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    Erratum
    • Misprints
      Uspekhi Mat. Nauk, 2011, 66:3(399), 207–208


    This publication is cited in the following articles:
    1. A. A. Aizenberg, V. M. Buchstaber, “Nerve complexes and moment–angle spaces of convex polytopes”, Proc. Steklov Inst. Math., 275 (2011), 15–46  mathnet  crossref  mathscinet  isi  elib  elib
    2. A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Agnarsson G., “The flag polynomial of the Minkowski sum of simplices”, Ann. Comb., 17:3 (2013), 401–426  crossref  mathscinet  zmath  isi
    4. N. Yu. Erokhovets, “Buchstaber invariant theory of simplicial complexes and convex polytopes”, Proc. Steklov Inst. Math., 286 (2014), 128–187  mathnet  crossref  crossref  isi  elib  elib
    5. G. Yu. Panina, I. Streinu, “Virtual polytopes”, Russian Math. Surveys, 70:6 (2015), 1105–1165  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. M. Buchstaber, I. Yu. Limonchenko, “Massey products, toric topology and combinatorics of polytopes”, Izv. Math., 83:6 (2019), 1081–1136  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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