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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Bibliographic Details
Published in:SIAM journal on discrete mathematics Vol. 25; no. 1; pp. 360 - 378
Main Authors: Ardila, Federico, Beck, Matthias, Hoşten, Serkan, Pfeifle, Julian, Seashore, Kim
Format: Journal Article Publication
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:
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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Summary: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]
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ISSN:0895-4801
1095-7146
DOI:10.1137/090749293