A generalization of Filliman duality

Author:
Greg Kuperberg

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3893-3899

MSC (2000):
Primary 52B45

Published electronically:
February 28, 2003

MathSciNet review:
1999938

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Abstract: Filliman duality expresses (the characteristic measure of) a convex polytope containing the origin as an alternating sum of simplices that share supporting hyperplanes with . The terms in the alternating sum are given by a triangulation of the polar body . The duality can lead to useful formulas for the volume of . A limiting case called Lawrence's algorithm can be used to compute the Fourier transform of .

In this note we extend Filliman duality to an involution on the space of polytopal measures on a finite-dimensional vector space, excluding polytopes that have a supporting hyperplane coplanar with the origin. As a special case, if is a convex polytope containing the origin, any realization of as a linear combination of simplices leads to a dual realization of .

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Additional Information

**Greg Kuperberg**

Affiliation:
Department of Mathematics, University of California-Davis, Davis, California 95616

Email:
greg@math.ucdavis.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-06957-0

Received by editor(s):
December 23, 2001

Received by editor(s) in revised form:
June 24, 2002, and July 10, 2002

Published electronically:
February 28, 2003

Additional Notes:
The author was supported by NSF grant DMS #0072342

Communicated by:
John R. Stembridge

Article copyright:
© Copyright 2003
American Mathematical Society