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Intrinsic volumes of polyhedral cones : a combinatorial perspective

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Amelunxen, D. and Lotz, Martin (2017) Intrinsic volumes of polyhedral cones : a combinatorial perspective. Discrete & Computational Geometry, 58 (2). pp. 371-409. ISSN 0179-5376.

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Abstract

The theory of intrinsic volumes of convex cones has recently found striking applications in areas such as convex optimization and compressive sensing. This article provides a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones. Direct derivations of the general Steiner formula, the conic analogues of the Brianchon–Gram–Euler and the Gauss–Bonnet relations, and the principal kinematic formula are given. In addition, a connection between the characteristic polynomial of a hyperplane arrangement and the intrinsic volumes of the regions of the arrangement, due to Klivans and Swartz, is generalized and some applications are presented.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Integral geometry, Cohomology operations, Combinatorial analysis, Polyhedral functions, Geometric probabilities
Journal or Publication Title: Discrete & Computational Geometry
Publisher: Springer New York LLC
ISSN: 0179-5376
Official Date: September 2017
Dates:
DateEvent
September 2017Published
5 July 2017Available
14 June 2017Accepted
Volume: 58
Number: 2
Page Range: pp. 371-409
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 22 July 2019
Date of first compliant Open Access: 29 July 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
CityU 21203315Hong Kong (China).‏ Legislative Councilhttp://viaf.org/viaf/136497858

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