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St. Petersburg Mathematical Journal

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Combinatorial identities for polyhedral cones


Author: R. Schneider
Original publication: Algebra i Analiz, tom 29 (2017), nomer 1.
Journal: St. Petersburg Math. J. 29 (2018), 209-221
MSC (2010): Primary 52B11; Secondary 52C35
DOI: https://doi.org/10.1090/spmj/1489
Published electronically: December 27, 2017
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Abstract: Some known relations for convex polyhedral cones, involving angles or conical intrinsic volumes, are superficially of a metric character, but have indeed a purely combinatorial core. This fact is strengthened in some cases, with implications for valuations on polyhedral cones, and is worked out in the case of the extended Klivans-Swartz formula.


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Additional Information

R. Schneider
Affiliation: Mathematisches Institut Albert-Ludwigs-Universität D-79104 Freiburg i. Br. Germany
Email: rolf.schneider@math.uni-freiburg.de

DOI: https://doi.org/10.1090/spmj/1489
Keywords: Polyhedral cone, angle sum relation, characteristic function, valuation, conical intrinsic volume, spherical Gauss--Bonnet relation, Klivans--Swartz formula
Received by editor(s): September 5, 2016
Published electronically: December 27, 2017
Dedicated: Dedicated to Professor Yuriĭ Dmitrievich Burago at the occasion of his 80th birthday
Article copyright: © Copyright 2017 American Mathematical Society

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