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An Alexander-type duality for valuations


Authors: Karim A. Adiprasito and Raman Sanyal
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
Published electronically: October 28, 2014
MathSciNet review: 3283669
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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
Email: adiprasito@ihes.fr, adiprssito@math.fu-berlin.de

Raman Sanyal
Affiliation: Fachbereich Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany
Email: sanyal@math.fu-berlin.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12366-5
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.