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Weighted Brianchon-Gram Decomposition

Open Access article
 Printed: Jun 2006
  • JosĂ© Agapito
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We give in this note a weighted version of Brianchon and Gram's decomposition for a simple polytope. We can derive from this decomposition the weighted polar formula of Agapito and a weighted version of Brion's theorem, in a manner similar to Haase, where the unweighted case is worked out. This weighted version of Brianchon and Gram' decomposition is a direct consequence of the ordinary Brianchon--Gram formula.
MSC Classifications: 52B show english descriptions unknown classification 52B 52B - unknown classification 52B

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