Geodesic
Weighted Brianchon-Gram Decomposition
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 161-169

Voir la notice de l'article provenant de la source Cambridge University Press

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's decomposition is a direct consequence of the ordinary Brianchon–Gram formula.
DOI : 10.4153/CMB-2006-017-x
Mots-clés : 52B 
Agapito, J. Weighted Brianchon-Gram Decomposition. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 161-169. doi: 10.4153/CMB-2006-017-x
@article{10_4153_CMB_2006_017_x,
     author = {Agapito, J.},
     title = {Weighted {Brianchon-Gram} {Decomposition}},
     journal = {Canadian mathematical bulletin},
     pages = {161--169},
     year = {2006},
     volume = {49},
     number = {2},
     doi = {10.4153/CMB-2006-017-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-017-x/}
}
TY  - JOUR
AU  - Agapito, J.
TI  - Weighted Brianchon-Gram Decomposition
JO  - Canadian mathematical bulletin
PY  - 2006
SP  - 161
EP  - 169
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-017-x/
DO  - 10.4153/CMB-2006-017-x
ID  - 10_4153_CMB_2006_017_x
ER  - 
%0 Journal Article
%A Agapito, J.
%T Weighted Brianchon-Gram Decomposition
%J Canadian mathematical bulletin
%D 2006
%P 161-169
%V 49
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-017-x/
%R 10.4153/CMB-2006-017-x
%F 10_4153_CMB_2006_017_x

[A] Agapito, J., A weighted version of quantization commutes with reduction for a toric manifold. In: Integer Points in Polyhedra: Geometry, Number Theory, Algebra, Optimization, Contemporary Mathematics 374, American Mathematical Society, Providence, RI, 2005, pp. 1–14. Google Scholar

[B] Barvinok, A., A Course in Convexity. Graduate Studies in Mathematics 54, American Mathematical Society, Providence, RI, 2002. Google Scholar

[Br] Brianchon, C. J., Théorème nouveau sur les polyèdres. J. École Polytechnique, 15(1837), 317–319. Google Scholar

[Br1] Brion, M., Points entiers dans les polyèdres convexes. Ann. Sci. École Norm. Sup. (4) 21(1988), 653–663. Google Scholar

[Br2] Brion, M., Polyèdres et réseaux, Enseign. Math (2) 38(1992), no. 1-2, 71–88. Google Scholar

[G] Gram, J. P., Om rumvinklerne i et polyeder. Tidsskrift for Math. (Copenhagen) (3) 4(1874), 161–163. Google Scholar

[H] Haase, C., Polar decomposition and Brion's theorem. In: Integer Points in Polyhedra: Geometry, Number Theory, Algebra, Optimization, Contemporary Mathematics 374, American Mathematical Society, Providence, RI, 2005, pp. 91–99. Google Scholar

[L] Lawrence, J., Polytope volume computation. Math. Comp. 57(1991), no. 195, 259–271. Google Scholar

[S] Shephard, G. C., An elementary proof of Gram's theorem for convex polytopes. Canad. J. Math. 19(1967), 1214–1217. Google Scholar

[V] Varchenko, A. N., Combinatorics and topology of the arrangement of affine hyperplanes in the real space. (English translation) Funct. Anal. Appl. 21(1987), no. 1, 9–19. Google Scholar

Cité par Sources :