ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9
Year 2016,
Volume: 4 Issue: 2, 124 - 131, 01.10.2016
Z. Akca
,
S. Ekmekcı
,
A. Bayar
Abstract
In this paper, we introduce Fano subplanes of the projective plane of order 9 coordinatized by elements of a left nearfield of order 9. We give an algorithm for checking\ Fano subplanes of this projective plane and apply the algorithm (implemented in C$\#$) to determine and classify Fano subplanes.
References
- [1] Akca, Z. - Gunaltili, I.- Guney, O., On the Fano subplanes of the left semield plane of order 9. Hacet. J. Math. Stat. 35 (2006), no. 1, 55-61.
- [2] Caliskan, C - Moorhouse, G. E., Subplanes of order 3 in Hughes planes, The Electronic Journal of Combinatorics 18 (2011), 1-8.
- [3] Ciftci, S - Kaya, R., On the Fano Subplanes in the Translation Plane of order 9, Doga-Tr. J. of Mathematics 14 (1990), 1-7.
- [4] Hall, M - Swift, J.D. - Killgrove, R., On projective planes of order nine, Math. Tables and Other Aids Comp. 13 (1959), 233-246.
- [5] Room, T.G - Kirkpatrick, P.B., Miniquaternion Geometry, London, Cambridge University Press, 177, (1971).
- [6] Veblen, O. - Wedderburn, J.H.M., Non-Desarguesian and non-Pascalian geometries, Trans. Amer. Math. Soc. 8 (1907), 379-388.
- [7] Tas, M., On the conguartions of projective plane of order 9 founded over left Hall system, ESOGU Sci. Enst., 2015.
Year 2016,
Volume: 4 Issue: 2, 124 - 131, 01.10.2016
Z. Akca
,
S. Ekmekcı
,
A. Bayar
References
- [1] Akca, Z. - Gunaltili, I.- Guney, O., On the Fano subplanes of the left semield plane of order 9. Hacet. J. Math. Stat. 35 (2006), no. 1, 55-61.
- [2] Caliskan, C - Moorhouse, G. E., Subplanes of order 3 in Hughes planes, The Electronic Journal of Combinatorics 18 (2011), 1-8.
- [3] Ciftci, S - Kaya, R., On the Fano Subplanes in the Translation Plane of order 9, Doga-Tr. J. of Mathematics 14 (1990), 1-7.
- [4] Hall, M - Swift, J.D. - Killgrove, R., On projective planes of order nine, Math. Tables and Other Aids Comp. 13 (1959), 233-246.
- [5] Room, T.G - Kirkpatrick, P.B., Miniquaternion Geometry, London, Cambridge University Press, 177, (1971).
- [6] Veblen, O. - Wedderburn, J.H.M., Non-Desarguesian and non-Pascalian geometries, Trans. Amer. Math. Soc. 8 (1907), 379-388.
- [7] Tas, M., On the conguartions of projective plane of order 9 founded over left Hall system, ESOGU Sci. Enst., 2015.