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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
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by Jesús A. De Loera, Xavier Goaoc, Frédéric Meunier and Nabil H. Mustafa PDF
Bull. Amer. Math. Soc. 56 (2019), 415-511 Request permission


We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as data science, game theory, graph theory, mathematical optimization, computational geometry, etc.
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Additional Information
  • Jesús A. De Loera
  • Affiliation: University of California, Department of Mathematics, Davis, California 95616
  • MR Author ID: 364032
  • ORCID: 0000-0002-9556-1112
  • Email:
  • Xavier Goaoc
  • Affiliation: Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
  • MR Author ID: 729132
  • Email:
  • Frédéric Meunier
  • Affiliation: Université Paris Est, CERMICS, ENPC, F-77454, Marne-la-Vallée, France
  • MR Author ID: 698556
  • Email:
  • Nabil H. Mustafa
  • Affiliation: Université Paris-Est, LIGM, Equipe A3SI, ESIEE Paris, Noisy le-Grand, France
  • MR Author ID: 737827
  • ORCID: 0000-0003-1046-6157
  • Email:
  • Received by editor(s): June 16, 2018
  • Published electronically: January 25, 2019
  • Additional Notes: The first author was partially supported by LabEx Bezout grant ANR-10-LABX-58 and also by NSF grant DMS-1522158.
    The second author was partially supported by Institut Universitaire de France.
    The fourth author was supported by ANR SAGA grant JCJC-14-CE25-0016-01.
  • © Copyright 2019 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 56 (2019), 415-511
  • MSC (2010): Primary 52Cxx, 57M99, 90Cxx, 91Axx
  • DOI:
  • MathSciNet review: 3974609