Root Polytopes and Growth Series of Root Lattices
نویسندگان
چکیده
منابع مشابه
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 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 Baak...
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The icosahedral quasicrystals of five-fold symmetry in two, three, and four dimensions are related to the corresponding regular polytopes exhibiting five-fold symmetry, namely the regular pentagon (H2 reflection group), the regular icosahedron 3,5 (H3 reflection group), and the regular four-dimensional polytope 3,3,5 (H4 reflection group). These quasicrystals exhibiting five-fold symmetry can b...
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چکیده ندارد.
15 صفحه اولCyclotomic Polytopes and Growth Series of Cyclotomic Lattices
The coordination sequence of a lattice L encodes the word-length function with respect toM , a set that generates L as a monoid. We investigate the coordination sequence of the cyclotomic lattice L = Z[ζm], where ζm is a primitive m th root of unity and where M is the set of all m roots of unity. We prove several conjectures by Parker regarding the structure of the rational generating function ...
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It is shown how root lattices and their reciprocals might serve as the right pool for the construction of quasicrystalline structure models. All non-periodic symmetries observed so far are covered in minimal embedding with maximal symmetry. For the construction of quasiperiodic tiling models by means of projection from higherdimensional periodic structures, the primitive hypercubic lattices are...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/090749293