Research Article
BibTex RIS Cite

A Note on Fano Configurations in the Projective Space PG(5,2)

Year 2021, Volume: 9 Issue: 1, 190 - 192, 28.04.2021

Abstract

Let $n\geq $ $2$ and let $U_{j}\mid j\in J$, with $|J|=n^{2}+n+1$, be a set of disjoint subspaces (of the same dimension) of some finite projective space $PG(N,q)$ with the property that the number of such subspaces in the span of any two such subspaces is always $n+1$ and the intersection of any two different such spans is always a subspace $U_{j}$ (so we have a projective plane of order $n$ with point set $U_{j}\mid j\in J.$) In this work we search for Fano configurations in PG(5,2) whose lines are 3-spaces and points are lines.

Supporting Institution

This work was supported by the Scientiic Research Projects Commission of Eskisehir Osmangazi University .

Project Number

2019-2542

References

  • [1] A. Akpınar, I. Dogan, E. Demirci, Z. Sena Gurel, and B. Boztemur, Some Remarks on a Class of Finite Projective Klingenberg Planes, Journal of Advances in Mathematics, vol. 14, no. 2 (2018), 7893–7902.
  • [2] A. Akpınar, B. C¸elik, and S. C¸iftc¸i, Cross Ratios and 6 Figures in some Moufang Klingenberg Planes, The Bulletin of the Belgian Mathematical Society-Simon Stevin, vol. 15, no. 1 (2008), 49–64.
  • [3] A. Bayar, Z. Akc¸a, E. Kahriman and S. Ekmekc¸i, On the complete arcs containing the quadrangles constructing the Fano planes of the left near field plane of order 9, New Trends in Mathematical Sciences, vol. 4, no. 4 (2016), 266–275.
  • [4] J. Hirschfeld, J. A.Thas, General Galois Geometries, Springer Monongraphs in Mathematics, 2016.
  • [5] S. Ekmekc¸i, Z. Akc¸a, H. Keskin and A. Bayar, Designing a Software Application for Fibered Fano Planes, International Journal of Mathematics and Statistics Invention (IJMSI), vol. 5, no. 1 (2017), 32–35.
  • [6] Z. Akca, I. Gunaltılı and G. Ozgur, On the Fano subplanes of the left semifield plane of order 9, Hacettepe Journal of Mathematics and Statistics, Volume 35 (1) (2006), 55 – 61.
  • [7] Z. Akça, S. Ekmekçi and A. Bayar, On the Fano subplanes of the left Hall plane of order 9, Konuralp Journal of Mathematics, vol. 4, no. 2 (2016), 124–131.
  • [8] Z. Akc¸a and I. Gunaltılı,¨ On the (k; 3) arcs of CPG(2; 25; 5) , Anadolu University Jounal of Science and Technology- B Theoretical Sciences, vol. 2, no.1 (2012), 21–27.
Year 2021, Volume: 9 Issue: 1, 190 - 192, 28.04.2021

Abstract

Project Number

2019-2542

References

  • [1] A. Akpınar, I. Dogan, E. Demirci, Z. Sena Gurel, and B. Boztemur, Some Remarks on a Class of Finite Projective Klingenberg Planes, Journal of Advances in Mathematics, vol. 14, no. 2 (2018), 7893–7902.
  • [2] A. Akpınar, B. C¸elik, and S. C¸iftc¸i, Cross Ratios and 6 Figures in some Moufang Klingenberg Planes, The Bulletin of the Belgian Mathematical Society-Simon Stevin, vol. 15, no. 1 (2008), 49–64.
  • [3] A. Bayar, Z. Akc¸a, E. Kahriman and S. Ekmekc¸i, On the complete arcs containing the quadrangles constructing the Fano planes of the left near field plane of order 9, New Trends in Mathematical Sciences, vol. 4, no. 4 (2016), 266–275.
  • [4] J. Hirschfeld, J. A.Thas, General Galois Geometries, Springer Monongraphs in Mathematics, 2016.
  • [5] S. Ekmekc¸i, Z. Akc¸a, H. Keskin and A. Bayar, Designing a Software Application for Fibered Fano Planes, International Journal of Mathematics and Statistics Invention (IJMSI), vol. 5, no. 1 (2017), 32–35.
  • [6] Z. Akca, I. Gunaltılı and G. Ozgur, On the Fano subplanes of the left semifield plane of order 9, Hacettepe Journal of Mathematics and Statistics, Volume 35 (1) (2006), 55 – 61.
  • [7] Z. Akça, S. Ekmekçi and A. Bayar, On the Fano subplanes of the left Hall plane of order 9, Konuralp Journal of Mathematics, vol. 4, no. 2 (2016), 124–131.
  • [8] Z. Akc¸a and I. Gunaltılı,¨ On the (k; 3) arcs of CPG(2; 25; 5) , Anadolu University Jounal of Science and Technology- B Theoretical Sciences, vol. 2, no.1 (2012), 21–27.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ziya Akça

Abdilkadir Altıntaş

Project Number 2019-2542
Publication Date April 28, 2021
Submission Date February 5, 2021
Acceptance Date February 27, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Akça, Z., & Altıntaş, A. (2021). A Note on Fano Configurations in the Projective Space PG(5,2). Konuralp Journal of Mathematics, 9(1), 190-192.
AMA Akça Z, Altıntaş A. A Note on Fano Configurations in the Projective Space PG(5,2). Konuralp J. Math. April 2021;9(1):190-192.
Chicago Akça, Ziya, and Abdilkadir Altıntaş. “A Note on Fano Configurations in the Projective Space PG(5,2)”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 190-92.
EndNote Akça Z, Altıntaş A (April 1, 2021) A Note on Fano Configurations in the Projective Space PG(5,2). Konuralp Journal of Mathematics 9 1 190–192.
IEEE Z. Akça and A. Altıntaş, “A Note on Fano Configurations in the Projective Space PG(5,2)”, Konuralp J. Math., vol. 9, no. 1, pp. 190–192, 2021.
ISNAD Akça, Ziya - Altıntaş, Abdilkadir. “A Note on Fano Configurations in the Projective Space PG(5,2)”. Konuralp Journal of Mathematics 9/1 (April 2021), 190-192.
JAMA Akça Z, Altıntaş A. A Note on Fano Configurations in the Projective Space PG(5,2). Konuralp J. Math. 2021;9:190–192.
MLA Akça, Ziya and Abdilkadir Altıntaş. “A Note on Fano Configurations in the Projective Space PG(5,2)”. Konuralp Journal of Mathematics, vol. 9, no. 1, 2021, pp. 190-2.
Vancouver Akça Z, Altıntaş A. A Note on Fano Configurations in the Projective Space PG(5,2). Konuralp J. Math. 2021;9(1):190-2.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.