Geodesic
Matroid automorphisms of the \(F_{4}\) root system
The electronic journal of combinatorics, Tome 14 (2007)
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Let $F_4$ be the root system associated with the 24-cell, and let $M(F_4)$ be the simple linear dependence matroid corresponding to this root system. We determine the automorphism group of this matroid and compare it to the Coxeter group $W$ for the root system. We find non-geometric automorphisms that preserve the matroid but not the root system.
DOI : 10.37236/996
Classification : 05B35, 20B25
Mots-clés : root system, 24-cell, simple linear dependence matroid, automorphism group, Coxeter group 
@article{10_37236_996,
     author = {Stephanie Fried and Aydin Gerek and Gary Gordon and Andrija Peruni\v{c}i\'c},
     title = {Matroid automorphisms of the {\(F_{4}\)} root system},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/996},
     zbl = {1160.05312},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/996/}
}
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Stephanie Fried; Aydin Gerek; Gary Gordon; Andrija Peruničić. Matroid automorphisms of the \(F_{4}\) root system. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/996

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