Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653544 | European Journal of Combinatorics | 2014 | 25 Pages |
Abstract
In the case of the root lattice E6, it is possible to give a more geometric description of the admissible sets of vectors U. We found that the set of admissible vectors, called free vectors, is described by the well-known configuration of 27 lines in a cubic surface. Based on a detailed study of the geometry of PV(E6), we give a simple characterization of the configurations of vectors U such that PV(E6)+Z(U) is a parallelotope. The enumeration yields 10 maximal families of vectors, which are presented by their description as regular matroids.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Mathieu Dutour SikiriÄ, Viacheslav Grishukhin, Alexander Magazinov,