The combinatorics of automorphisms and opposition in generalised polygons
- Author
- James Parkinson, Beukje Temmermans and Hendrik Van Maldeghem (UGent)
- Organization
- Abstract
- We investigate the combinatorial interplay between automorphisms and opposition in (primarily finite) generalised polygons. We provide restrictions on the fixed element structures of automorphisms of a generalised polygon mapping no chamber to an opposite chamber. Furthermore, we give a complete classification of automorphisms of finite generalised polygons which map at least one point and at least one line to an opposite, but map no chamber to an opposite chamber. Finally, we show that no automorphism of a finite thick generalised polygon maps all chambers to opposite chambers, except possibly in the case of generalised quadrangles with coprime parameters.
- Keywords
- Phan theory, COLLINEATIONS, projective planes, generalised polygons, domestic automorphisms, HEXAGON, ORDER, QUADRANGLES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-7002630
- MLA
- Parkinson, James, et al. “The Combinatorics of Automorphisms and Opposition in Generalised Polygons.” ANNALS OF COMBINATORICS, vol. 19, no. 3, 2015, pp. 567–619, doi:10.1007/s00026-015-0277-6.
- APA
- Parkinson, J., Temmermans, B., & Van Maldeghem, H. (2015). The combinatorics of automorphisms and opposition in generalised polygons. ANNALS OF COMBINATORICS, 19(3), 567–619. https://doi.org/10.1007/s00026-015-0277-6
- Chicago author-date
- Parkinson, James, Beukje Temmermans, and Hendrik Van Maldeghem. 2015. “The Combinatorics of Automorphisms and Opposition in Generalised Polygons.” ANNALS OF COMBINATORICS 19 (3): 567–619. https://doi.org/10.1007/s00026-015-0277-6.
- Chicago author-date (all authors)
- Parkinson, James, Beukje Temmermans, and Hendrik Van Maldeghem. 2015. “The Combinatorics of Automorphisms and Opposition in Generalised Polygons.” ANNALS OF COMBINATORICS 19 (3): 567–619. doi:10.1007/s00026-015-0277-6.
- Vancouver
- 1.Parkinson J, Temmermans B, Van Maldeghem H. The combinatorics of automorphisms and opposition in generalised polygons. ANNALS OF COMBINATORICS. 2015;19(3):567–619.
- IEEE
- [1]J. Parkinson, B. Temmermans, and H. Van Maldeghem, “The combinatorics of automorphisms and opposition in generalised polygons,” ANNALS OF COMBINATORICS, vol. 19, no. 3, pp. 567–619, 2015.
@article{7002630,
abstract = {{We investigate the combinatorial interplay between automorphisms and opposition in (primarily finite) generalised polygons. We provide restrictions on the fixed element structures of automorphisms of a generalised polygon mapping no chamber to an opposite chamber. Furthermore, we give a complete classification of automorphisms of finite generalised polygons which map at least one point and at least one line to an opposite, but map no chamber to an opposite chamber. Finally, we show that no automorphism of a finite thick generalised polygon maps all chambers to opposite chambers, except possibly in the case of generalised quadrangles with coprime parameters.}},
author = {{Parkinson, James and Temmermans, Beukje and Van Maldeghem, Hendrik}},
issn = {{0218-0006}},
journal = {{ANNALS OF COMBINATORICS}},
keywords = {{Phan theory,COLLINEATIONS,projective planes,generalised polygons,domestic automorphisms,HEXAGON,ORDER,QUADRANGLES}},
language = {{eng}},
number = {{3}},
pages = {{567--619}},
title = {{The combinatorics of automorphisms and opposition in generalised polygons}},
url = {{http://doi.org/10.1007/s00026-015-0277-6}},
volume = {{19}},
year = {{2015}},
}
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