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2015.115: Intrinsic Volumes of Polyhedral Cones: A combinatorial perspective

2015.115: Dennis Amelunxen and Martin Lotz (2015) Intrinsic Volumes of Polyhedral Cones: A combinatorial perspective.

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Abstract

These notes provide a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones. Streamlined 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 presented.

Item Type:MIMS Preprint
Uncontrolled Keywords:Convex geometry, polyhedra, cones, intrinsic volumes, integral geometry, geometric probability, kinematic formula, Gauss-Bonnet, hyperplane arrangements
Subjects:MSC 2000 > 52 Convex and discrete geometry
MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2015.115
Deposited By:Dr. Martin Lotz
Deposited On:19 December 2015

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