Highest rank of a polytope for An
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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.
Cameron , P J , Fernandes , M E , Leemans , D & Mixer , M 2017 , ' Highest rank of a polytope for A n ' Proceedings of the London Mathematical Society , vol 115 , no. 1 , pp. 135-176 . DOI: 10.1112/plms.12039
Proceedings of the London Mathematical Society
© 2017, London Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at academic.oup.com/plms / https://doi.org/10.1112/plms.12039
This research was supported by a Marsden grant (UOA1218) of the Royal Society of New Zealand, and by the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.
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