One-point extensions of generalized hexagons and octagons
- Author
- Hans Cuypers, An De Wispelaere and Hendrik Van Maldeghem (UGent)
- Organization
- Abstract
- In this note, we prove the uniqueness of the one-point extension S of a generalized hexagon of order 2 and prove the nonexistence of such an extension S of any other finite generalized hexagon of classical order, different from the one of order 2, and of the known finite generalized octagons provided the following property holds: for any three points x, y and z of S, the graph-theoretic distance from y to z in the derived generalized hexagon S-x is the same as the distance from x to z in S-y.
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-686389
- MLA
- Cuypers, Hans, et al. “One-Point Extensions of Generalized Hexagons and Octagons.” Discrete Mathematics, vol. 309, no. 2, 2009, pp. 341–53, doi:10.1016/j.disc.2007.12.015.
- APA
- Cuypers, H., De Wispelaere, A., & Van Maldeghem, H. (2009). One-point extensions of generalized hexagons and octagons. Discrete Mathematics, 309(2), 341–353. https://doi.org/10.1016/j.disc.2007.12.015
- Chicago author-date
- Cuypers, Hans, An De Wispelaere, and Hendrik Van Maldeghem. 2009. “One-Point Extensions of Generalized Hexagons and Octagons.” Discrete Mathematics 309 (2): 341–53. https://doi.org/10.1016/j.disc.2007.12.015.
- Chicago author-date (all authors)
- Cuypers, Hans, An De Wispelaere, and Hendrik Van Maldeghem. 2009. “One-Point Extensions of Generalized Hexagons and Octagons.” Discrete Mathematics 309 (2): 341–353. doi:10.1016/j.disc.2007.12.015.
- Vancouver
- 1.Cuypers H, De Wispelaere A, Van Maldeghem H. One-point extensions of generalized hexagons and octagons. Discrete Mathematics. 2009;309(2):341–53.
- IEEE
- [1]H. Cuypers, A. De Wispelaere, and H. Van Maldeghem, “One-point extensions of generalized hexagons and octagons,” Discrete Mathematics, vol. 309, no. 2, pp. 341–353, 2009.
@article{686389,
abstract = {{In this note, we prove the uniqueness of the one-point extension S of a generalized hexagon of order 2 and prove the nonexistence of such an extension S of any other finite generalized hexagon of classical order, different from the one of order 2, and of the known finite generalized octagons provided the following property holds: for any three points x, y and z of S, the graph-theoretic distance from y to z in the derived generalized hexagon S-x is the same as the distance from x to z in S-y.}},
author = {{Cuypers, Hans and De Wispelaere, An and Van Maldeghem, Hendrik}},
issn = {{0012-365X}},
journal = {{Discrete Mathematics}},
language = {{eng}},
number = {{2}},
pages = {{341--353}},
title = {{One-point extensions of generalized hexagons and octagons}},
url = {{http://doi.org/10.1016/j.disc.2007.12.015}},
volume = {{309}},
year = {{2009}},
}
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