| Títol: | Root polytopes and growth series of root lattices |
| Autor: | Ardila, Federico
Beck, Matthias
Hosten, Serkan
Pfeifle, Julián
Seashore, Kim |
| Altres autors/autores: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
| Matèries: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
Combinatorial analysis
Discrete geometry
Number theory
Anàlisi combinatòria
Geometria discreta
Nombres, Teoria dels
Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry
Classificació AMS::05 Combinatorics::05A Enumerative combinatorics
Classificació AMS::11 Number theory::11H Geometry of numbers |
| Tipus de document: | Article |
| Descripció: | The convex hull of the roots of a classical root lattice is called a root polytope. We determine explicit unimodular triangulations of the boundaries of the root polytopes associated to the root lattices $A_n$, $C_n$, and $D_n$, and we compute their $f$- and $h$-vectors. This leads us to recover formulae for the growth series of these root lattices, which were first conjectured by Conway, Mallows, and Sloane and Baake and Grimm and were proved by Conway and Sloane and Bacher, de la Harpe, and Venkov. We also prove the formula for the growth series of the root lattice $B_n$, which requires a modification of our technique. |
| Altres identificadors i accés: | Ardila, F. [et al.]. Root polytopes and growth series of root lattices. "SIAM journal on discrete mathematics", 2011, vol. 25, núm. 1, p. 360-378.
0895-4801
http://hdl.handle.net/2117/11800
10.1137/090749293 |
| Disponible al dipòsit: | E-prints UPC
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