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SOME GEOMETRIC STRUCTURES RELATED TO DESARGUES CONFIGURATION IN PG(2,5)

Year 2024, Volume: 25 Issue: 3, 511 - 518, 30.09.2024
https://doi.org/10.18038/estubtda.1525364

Abstract

In this study, we investigate geometric structures related to Desargues configuration in PG(2,5), using an algorithm implemented in C#. We determine different six complete (11,3)-arcs containing Desargues configuration, a (6,2)-arc not containing Desargues configuration, a complete (16,4)- arc, and an affine plane in PG(2,5).

References

  • [1] Hirschfeld JWP, Thas JA. General Galois Geometries, Springer Monographs in Mathematics. Springer- Verlag London, 2016.
  • [2] Bayar A, Akca Z, Altintas E, Ekmekci S. On the complete arcs containing the quadrangles constructing the Fano planes of the left near field plane of order 9. New Trends in Mathematical Science. 2016, 4(4), 266-266.
  • [3] Ekmekci S, Bayar A, Altintas E, Akca Z. On the Complete (k,2)- Arcs of the Hall Plane of Order 9. International Journal of Advanced Research in Computer Science and Software Engineering. 2016, 6 (10), 282-288.
  • [4] Akca Z, Ekmekci S, Bayar A. On Fano Configurations of the Left Hall Plane of order 9. Konuralp journal of mathematics. 2016, 4 (2), 116-123.
  • [5] Akca Z, Altıntas A. A Note on Fano Configurations in the Projective Space PG(5,2), Konuralp Journal of Mathematics. 2021, 9(1), 190-192.
  • [6] Akca Z. A numerical computation of (k, 3)-arcs in the left semifield plane order 9, International Electronic Journal of Geometry. 2011, 4(2), 13-21.
  • [7] Akca Z, Günaltılı I On the (k, 3)- arcs of CPG (2,25,5), Anadolu University Jounal of Science and Technology-B Theoretical Sciences. 2012, 1(0), 21-27.
  • [8] Qassim BA. The construction for the arcs (8,4)-from the two arcs (7,4)-in PG (2,q), q=5. J. Phys.: Conf. Ser. 2020, 1664012039.
  • [9] Hirschfeld JWP, Thas JA. General Galois Geometries, The Charendon Press, Oxford, 1991.
  • [10] Hirschfeld JWP, Voloch JF. Group-arcs of prime order on cubic curves, Finite Geometry and Combinatorics, 2015, 191, 177-185.
  • [11] Hirschfeld JWP. Projective Geometries over Finite Fields, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, second edition, 1998.
  • [12] Hall M. Projective planes. Trans. Am. Math. Soc. 1943, 54, 229-277 .
  • [13] Hall M, Swift Jr, J.D, Killgrove R. On projective planes of order nine.Math.Tables and Other Aids Comp. 1959, 13, 233-246 .
  • [14] Pichanick EVD, Hirschfeld JWP. Bounds for arcs of arbitrary degree in finite Desarguesian Planes. Journal of Combinatorial Designs. 2016, 24(4), 184-196.
  • [15] Altıntas E, Bayar A. Complete (k,2)-Arcs in the Projective Plane Order 5. Hagia Sophia Journal of Geometry. 2023, 5(1), 11-14.
Year 2024, Volume: 25 Issue: 3, 511 - 518, 30.09.2024
https://doi.org/10.18038/estubtda.1525364

Abstract

References

  • [1] Hirschfeld JWP, Thas JA. General Galois Geometries, Springer Monographs in Mathematics. Springer- Verlag London, 2016.
  • [2] Bayar A, Akca Z, Altintas E, Ekmekci S. On the complete arcs containing the quadrangles constructing the Fano planes of the left near field plane of order 9. New Trends in Mathematical Science. 2016, 4(4), 266-266.
  • [3] Ekmekci S, Bayar A, Altintas E, Akca Z. On the Complete (k,2)- Arcs of the Hall Plane of Order 9. International Journal of Advanced Research in Computer Science and Software Engineering. 2016, 6 (10), 282-288.
  • [4] Akca Z, Ekmekci S, Bayar A. On Fano Configurations of the Left Hall Plane of order 9. Konuralp journal of mathematics. 2016, 4 (2), 116-123.
  • [5] Akca Z, Altıntas A. A Note on Fano Configurations in the Projective Space PG(5,2), Konuralp Journal of Mathematics. 2021, 9(1), 190-192.
  • [6] Akca Z. A numerical computation of (k, 3)-arcs in the left semifield plane order 9, International Electronic Journal of Geometry. 2011, 4(2), 13-21.
  • [7] Akca Z, Günaltılı I On the (k, 3)- arcs of CPG (2,25,5), Anadolu University Jounal of Science and Technology-B Theoretical Sciences. 2012, 1(0), 21-27.
  • [8] Qassim BA. The construction for the arcs (8,4)-from the two arcs (7,4)-in PG (2,q), q=5. J. Phys.: Conf. Ser. 2020, 1664012039.
  • [9] Hirschfeld JWP, Thas JA. General Galois Geometries, The Charendon Press, Oxford, 1991.
  • [10] Hirschfeld JWP, Voloch JF. Group-arcs of prime order on cubic curves, Finite Geometry and Combinatorics, 2015, 191, 177-185.
  • [11] Hirschfeld JWP. Projective Geometries over Finite Fields, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, second edition, 1998.
  • [12] Hall M. Projective planes. Trans. Am. Math. Soc. 1943, 54, 229-277 .
  • [13] Hall M, Swift Jr, J.D, Killgrove R. On projective planes of order nine.Math.Tables and Other Aids Comp. 1959, 13, 233-246 .
  • [14] Pichanick EVD, Hirschfeld JWP. Bounds for arcs of arbitrary degree in finite Desarguesian Planes. Journal of Combinatorial Designs. 2016, 24(4), 184-196.
  • [15] Altıntas E, Bayar A. Complete (k,2)-Arcs in the Projective Plane Order 5. Hagia Sophia Journal of Geometry. 2023, 5(1), 11-14.
There are 15 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Articles
Authors

Elif Altıntaş Kahriman 0000-0002-3454-0326

Ayşe Bayar 0000-0002-2210-5423

Publication Date September 30, 2024
Submission Date July 31, 2024
Acceptance Date September 16, 2024
Published in Issue Year 2024 Volume: 25 Issue: 3

Cite

AMA Altıntaş Kahriman E, Bayar A. SOME GEOMETRIC STRUCTURES RELATED TO DESARGUES CONFIGURATION IN PG(2,5). Estuscience - Se. September 2024;25(3):511-518. doi:10.18038/estubtda.1525364