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Highest rank of a polytope for An

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Cameron_2017_Highest_PLMS_AAM.pdf (436.0Kb)
Date
04/07/2017
Author
Cameron, Peter J.
Fernandes, Maria Elisa
Leemans, Dimitri
Mixer, Mark
Keywords
Abstract regular polytypes
String C-groups
Alternating groups
Permutation groups
QA Mathematics
Mathematics(all)
T-NDAS
BDC
R2C
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Abstract
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.
Citation
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 . https://doi.org/10.1112/plms.12039
Publication
Proceedings of the London Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1112/plms.12039
ISSN
0024-6115
Type
Journal article
Rights
© 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 https://doi.org/10.1112/plms.12039
Description
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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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/10678

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