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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.
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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 | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of 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: |
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| Volume: | 58 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 371-409 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access | ||||||||
| RIOXX Funder/Project Grant: |
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