On extreme forms in dimension 8
- [1] J.W. Goethe-Universitaet Fb. Mathematik u. Informatik 60054 Frankfurt am Main
Journal de Théorie des Nombres de Bordeaux (2006)
- Volume: 18, Issue: 3, page 677-682
- ISSN: 1246-7405
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topRiener, Cordian. "On extreme forms in dimension 8." Journal de Théorie des Nombres de Bordeaux 18.3 (2006): 677-682. <http://eudml.org/doc/249637>.
@article{Riener2006,
abstract = {A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension $8$ has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for example $30$ out of the $33$ in dimension $7$). This is no longer the case in dimension $8$: up to similarity, there are only $2408$ extreme $8$-dimensional lattices.},
affiliation = {J.W. Goethe-Universitaet Fb. Mathematik u. Informatik 60054 Frankfurt am Main},
author = {Riener, Cordian},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {extreme lattices; eutactic lattices; perfect lattices},
language = {eng},
number = {3},
pages = {677-682},
publisher = {Université Bordeaux 1},
title = {On extreme forms in dimension 8},
url = {http://eudml.org/doc/249637},
volume = {18},
year = {2006},
}
TY - JOUR
AU - Riener, Cordian
TI - On extreme forms in dimension 8
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2006
PB - Université Bordeaux 1
VL - 18
IS - 3
SP - 677
EP - 682
AB - A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension $8$ has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for example $30$ out of the $33$ in dimension $7$). This is no longer the case in dimension $8$: up to similarity, there are only $2408$ extreme $8$-dimensional lattices.
LA - eng
KW - extreme lattices; eutactic lattices; perfect lattices
UR - http://eudml.org/doc/249637
ER -
References
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- G. Voronoi, Nouvelles applications des paramètres continus à la théorie des formes quadratiques: 1. Sur quelques propriétés des formes quadratiques parfaites. J. reine angew. Math. 133 (1908), 97–178. Zbl38.0261.01
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