Coincidence rotations of the root lattice $A_4$

Details Coincidence rotations of the root lattice $A_4$ Coincidence rotations of the root lattice $A_4$

2007-09-10

arxiv.org/abs/0709.1341v1

European Journal of Combinatorics 29 (2008) 1808-1819

Mathematics

Metric Geometry

13 pages, 1 figure

Scientific paper

10.1016/j.ejc.2008.01.012

The coincidence site lattices of the root lattice $A_4$ are considered, and the statistics of the corresponding coincidence rotations according to their indices is expressed in terms of a Dirichlet series generating function. This is possible via an embedding of $A_4$ into the icosian ring with its rich arithmetic structure, which recently (arXiv:math.MG/0702448) led to the classification of the similar sublattices of $A_4$.

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