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

Year 2024, Volume: 25 Issue: 3, 511 - 518, 30.09.2024

Elif Altıntaş Kahriman , Ayşe Bayar

https://doi.org/10.18038/estubtda.1525364

Cited By: 1

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).

Keywords

projective plane , complete arc , (k,n)-arc , Desargues Configuration

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.