Polar decomposition and Brion’s theorem | Zendy

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Polar decomposition and Brion’s theorem

Author(s) -

Christian Haase

Publication year - 2005

Publication title -

contemporary mathematics - american mathematical society

Language(s) - English

Resource type - Reports

SCImago Journal Rank - 0.106

H-Index - 12

eISSN - 1098-3627

pISSN - 0271-4132

DOI - 10.1090/conm/374/06901

Subject(s) - mathematics , polytope , polar decomposition , combinatorics , polar , decomposition , vertex (graph theory) , regular polygon , decomposition theorem , convex polytope , lattice (music) , convex set , geometry , physics , graph , chemistry , convex optimization , quantum mechanics , organic chemistry , acoustics

In this note we point out the relation between Brion's formula for the lattice point generating function of a convex polytope in terms of the vertex cones [Brion1988] on the one hand, and the polar decomposition \`a la Lawrence/Varchenko [Lawrence1991, Varchenko1987] on the other. We then go on to prove a version of polar decomposition for non-simple polytopes.

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