descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2011Embargo end date: 01 Jan 2008 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 25, pages 360-378 (issn: 0895-4801, eissn: 1095-7146,

Authors: Ardila, Federico; Beck, Matthias; Hosten, Serkan; Pfeifle, Julián; Seashore, Kim;

doi: 10.1137/090749293 , 10.48550/arxiv.0809.5123

arXiv: http://arxiv.org/abs/0809.5123

handle: 2117/11800

Root Polytopes and Growth Series of Root Lattices

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Abstract

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 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-Sloane and Baake-Grimm and proved by Conway-Sloane and Bacher-de la Harpe-Venkov.

17 pages, 3 figures

Related Organizations

Universitat Politècnica de Catalunya
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Keywords

Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry, Teoria dels, Combinatorial analysis, Classificació AMS::05 Combinatorics::05A Enumerative combinatorics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta, Discrete geometry, Nombres, Teoria dels, :52 Convex and discrete geometry::52C Discrete geometry [Classificació AMS], :Matemàtiques i estadística::Geometria::Geometria convexa i discreta [Àrees temàtiques de la UPC], Geometria discreta, Classificació AMS::11 Number theory::11H Geometry of numbers, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), :11 Number theory::11H Geometry of numbers [Classificació AMS], Nombres, Number theory, FOS: Mathematics, :05 Combinatorics::05A Enumerative combinatorics [Classificació AMS], Mathematics - Combinatorics, Combinatorics (math.CO), 05A15, 05E15, 11H06, 13D40, 14M25, 52B20, 52C07, Anàlisi combinatòria

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