Root polytopes and growth series of root lattices
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 for...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/11800 |
| Acceso en línea: | https://hdl.handle.net/2117/11800 https://dx.doi.org/10.1137/090749293 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta |
| Sumario: | 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. |
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