no. 3
Séries de croissance et polynômes d'Ehrhart associés aux réseaux de racines
Annales de l'Institut Fourier, Tome 49 (1999) no. 3, pp. 727-762.

Étant donnés un système de racines R d’une des familles A, B, C, D, F, G et le groupe abélien libre qu’il engendre, on calcule explicitement la série de croissance de ce groupe relativement à R. Les résultats s’interprètent en termes du polynôme d’Ehrhart de l’enveloppe convexe de R.

Given a root system R in one of the families A, B, C, D, F, G and the free abelian group that it generates, we compute explicitly the growth series of this group with respect to R. The results can be interpreted in terms of the Ehrhart polynomial of the convex hull of R.

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     author = {Bacher, Roland and Harpe, P. de la and Venkov, Boris},
     title = {S\'eries de croissance et polyn\^omes {d'Ehrhart} associ\'es aux r\'eseaux de racines},
     journal = {Annales de l'Institut Fourier},
     pages = {727--762},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {3},
     year = {1999},
     doi = {10.5802/aif.1689},
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     url = {http://archive.numdam.org/articles/10.5802/aif.1689/}
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Bacher, Roland; Harpe, P. de la; Venkov, Boris. Séries de croissance et polynômes d'Ehrhart associés aux réseaux de racines. Annales de l'Institut Fourier, Tome 49 (1999) no. 3, pp. 727-762. doi : 10.5802/aif.1689. http://archive.numdam.org/articles/10.5802/aif.1689/

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