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Dergiler / Konuralp Journal of Mathematics / 2016 / Volume: 4 Issue: 2

ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9

Z. Akca
S. Ekmekcı
A. Bayar
Sayfa
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Yayın Tarihi
2016-10-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we introduce Fano subplanes of the projective plane of order 9 coordinatized by elements of a left nearfield of order 9.
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Temel Bulgular & Veri:In this paper, we introduce Fano subplanes of the projective plane of order 9 coordinatized by elements of a left nearfield of order 9.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Near field · Projective plane · Fano plane

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.

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Bu Makaleye Atıf Yap

Akca, Z., Ekmekcı, S., Bayar, A. (2016). ON FANO CONFIGURATIONS OF THE LEFT HALL PLANE OF ORDER 9. Konuralp Journal of Mathematics, Volume: 4 Issue: 2. https://ajindex.com/articles/1521875

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Kaynakça (7)

  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.