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Root Polytopes and Growth Series of Root Lattices

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Názov:	Root Polytopes and Growth Series of Root Lattices
Autori:	Ardila, Federico, Beck, Matthias, Hosten, Serkan, Pfeifle, Julián, Seashore, Kim
Prispievatelia:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
Zdroj:	Recercat. Dipósit de la Recerca de Catalunya instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC)
Publication Status:	Preprint
Informácie o vydavateľovi:	Society for Industrial & Applied Mathematics (SIAM), 2011.
Rok vydania:	2011
Predmety:	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), 01 natural sciences, 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, 0101 mathematics, Anàlisi combinatòria
Popis:	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
Druh dokumentu:	Article
Popis súboru:	application/pdf
Jazyk:	English
ISSN:	1095-7146 0895-4801
DOI:	10.1137/090749293
DOI:	10.48550/arxiv.0809.5123
Prístupová URL adresa:	https://upcommons.upc.edu/bitstream/2117/11800/1/root_polytopes_growth.pdf http://arxiv.org/abs/0809.5123 http://hdl.handle.net/2117/11800 https://dblp.uni-trier.de/db/journals/siamdm/siamdm25.html#ArdilaBHPS11 http://math.sfsu.edu/federico/Articles/rootpolytopes.pdf https://upcommons.upc.edu/bitstream/2117/11800/1/root_polytopes_growth.pdf https://epubs.siam.org/doi/abs/10.1137/090749293 https://upcommons.upc.edu/handle/2117/11800 https://core.ac.uk/display/41764429 https://hdl.handle.net/2117/11800 https://doi.org/10.1137/090749293
Rights:	CC BY NC ND arXiv Non-Exclusive Distribution
Prístupové číslo:	edsair.doi.dedup.....378adcfe65d4c60bbcc25a7b41a2d003
Databáza:	OpenAIRE

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Abstrakt:	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.<br />17 pages, 3 figures
ISSN:	10957146 08954801
DOI:	10.1137/090749293