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 An, Cn, and Dn, and we compute their f- and h-vectors. This leads us to recover formulae for the...

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Vydáno v:	SIAM journal on discrete mathematics Ročník 25; číslo 1; s. 360 - 378
Hlavní autoři:	Ardila, Federico, Beck, Matthias, Hoşten, Serkan, Pfeifle, Julian, Seashore, Kim
Médium:	Journal Article Publikace
Jazyk:	angličtina
Vydáno:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Témata:	05 Combinatorics 05A Enumerative combinatorics 11 Number theory 11H Geometry of numbers 52 Convex and discrete geometry 52C Discrete geometry Algebra Anàlisi combinatòria Boundaries Classificació AMS Combinatorial analysis Combinatorics Combinatorics. Ordered structures Convex and discrete geometry Discrete geometry Exact sciences and technology Geometria Geometria convexa i discreta Geometria discreta Geometry Hulls Hulls (structures) Lattice theory Lattices Matemàtiques i estadística Mathematical analysis Mathematical models Mathematics Nombres, Teoria dels Number theory Order, lattices, ordered algebraic structures Polynomials Polytopes Roots Sciences and techniques of general use Studies Àrees temàtiques de la UPC Polynomial Polytope f-vector Modification Triangulation 11H06 Lattice 52C07 Convex hull coordinator polynomial growth series Discrete mathematics root polytope unimodular triangulation Vector 05A15 root lattice
ISSN:	0895-4801, 1095-7146
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Popis
Shrnutí:	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 An, Cn, and Dn, 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 Bn, which requires a modification of our technique. [PUBLICATION ABSTRACT]
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0895-4801 1095-7146
DOI:	10.1137/090749293