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ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9

Year 2016, Volume: 4 Issue: 2, 124 - 131, 01.10.2016

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 semi eld 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 con guartions 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

Abstract

References

  • [1] Akca, Z. - Gunaltili, I.- Guney,  O., On the Fano subplanes of the left semi eld 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 con guartions of projective plane of order 9 founded over left Hall system, ESOGU Sci. Enst., 2015.
There are 7 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Z. Akca

S. Ekmekcı

A. Bayar

Publication Date October 1, 2016
Submission Date July 16, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Akca, Z., Ekmekcı, S., & Bayar, A. (2016). ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9. Konuralp Journal of Mathematics, 4(2), 124-131.
AMA Akca Z, Ekmekcı S, Bayar A. ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9. Konuralp J. Math. October 2016;4(2):124-131.
Chicago Akca, Z., S. Ekmekcı, and A. Bayar. “ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 124-31.
EndNote Akca Z, Ekmekcı S, Bayar A (October 1, 2016) ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9. Konuralp Journal of Mathematics 4 2 124–131.
IEEE Z. Akca, S. Ekmekcı, and A. Bayar, “ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9”, Konuralp J. Math., vol. 4, no. 2, pp. 124–131, 2016.
ISNAD Akca, Z. et al. “ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9”. Konuralp Journal of Mathematics 4/2 (October 2016), 124-131.
JAMA Akca Z, Ekmekcı S, Bayar A. ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9. Konuralp J. Math. 2016;4:124–131.
MLA Akca, Z. et al. “ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 124-31.
Vancouver Akca Z, Ekmekcı S, Bayar A. ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9. Konuralp J. Math. 2016;4(2):124-31.
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