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Highest rank of a polytope for An

par Cameron, Peter;Fernandes, Maria Elisa;Leemans, Dimitri ;Mixer, Mark
Référence Proceedings of the London Mathematical Society, 115, 1, page (135-176)
Publication Publié, 2017-07

Article révisé par les pairs

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Résumé :

We prove that the highest rank of a string C-group constructed from an alternating group An is 3 if n=5, 4 if n=9, 5 if n=10, 6 if n=11, and ⌊(n-1)/2⌋ if n ≥ 12. Moreover, if n=3,4,6,7, or 8, the group An is not a string C-group. This solves a conjecture made by the last three authors in 2012.