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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An Alexander-type duality for valuations
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by Karim A. Adiprasito and Raman Sanyal PDF
Proc. Amer. Math. Soc. 143 (2015), 833-843 Request permission

Abstract:

We prove an Alexander-type duality for valuations for certain subcomplexes in the boundary of polyhedra. These strengthen and simplify results of Stanley (1974) and Miller–Reiner (2005). We give a generalization of Brion’s theorem for this relative situation, and we discuss the topology of the possible subcomplexes for which the duality relation holds.
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Additional Information
  • Karim A. Adiprasito
  • Affiliation: Institut des Hautes Études Scientifiques, Paris, France
  • MR Author ID: 963585
  • Email: adiprasito@ihes.fr, adiprssito@math.fu-berlin.de
  • Raman Sanyal
  • Affiliation: Fachbereich Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany
  • MR Author ID: 856938
  • Email: sanyal@math.fu-berlin.de
  • Received by editor(s): April 13, 2013
  • Published electronically: October 28, 2014
  • Additional Notes: The first author has been supported by the DFG within the research training group “Methods for Discrete Structures” (GRK1408) and by the Romanian NASR, CNCS — UEFISCDI, project PN-II-ID-PCE-2011-3-0533.
    The second author has been supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n$^\mathrm {o}$ 247029.
  • Communicated by: Jim Haglund
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 833-843
  • MSC (2010): Primary 52B45, 57Q99, 52C07, 55U30
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12366-5
  • MathSciNet review: 3283669