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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Mixing and monodromy of abstract polytopes
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by B. Monson, Daniel Pellicer and Gordon Williams PDF
Trans. Amer. Math. Soc. 366 (2014), 2651-2681 Request permission

Abstract:

The monodromy group $\mathrm {Mon}(\mathcal {P})$ of an $n$-polytope $\mathcal {P}$ encodes the combinatorial information needed to construct $\mathcal {P}$. By applying tools such as mixing, a natural group-theoretic operation, we develop various criteria for $\mathrm {Mon}(\mathcal {P})$ itself to be the automorphism group of a regular $n$-polytope $\mathcal {R}$. We examine what this can say about regular covers of $\mathcal {P}$, study a peculiar example of a $4$-polytope with infinitely many distinct, minimal regular covers, and then conclude with a brief application of our methods to chiral polytopes.
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Additional Information
  • B. Monson
  • Affiliation: Department of Mathematics, University of New Brunswick, Fredericton, New Bruns- wick, Canada
  • Email: bmonson@unb.ca
  • Daniel Pellicer
  • Affiliation: Instituto de Matematicas, UNAM Morelia, Morelia, Michoacán, México
  • Email: pellicer@matmor.unam.mx
  • Gordon Williams
  • Affiliation: Department of Mathematics, University of Alaska Fairbanks, Fairbanks, Alaska 99775
  • MR Author ID: 694060
  • Email: giwilliams@alaska.edu
  • Received by editor(s): June 19, 2012
  • Received by editor(s) in revised form: September 6, 2012
  • Published electronically: November 4, 2013
  • Additional Notes: The first author was supported by NSERC of Canada Discovery Grant # 4818.
    The second author was supported by grants PAPIIT (IAOCD) # IA101311 and PAPIIT #IB100312.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 2651-2681
  • MSC (2010): Primary 51M20; Secondary 20F55
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05954-5
  • MathSciNet review: 3165650