COMPLETE (k,3)-ARCS CONTAINING COMPLETE QUADRANGLE VERTICES IN PG(2,4): STRUCTURAL ANALYSIS BASED ON DIAGONAL POINT INCLUSION.
Saved in:
| Title: | COMPLETE (k,3)-ARCS CONTAINING COMPLETE QUADRANGLE VERTICES IN PG(2,4): STRUCTURAL ANALYSIS BASED ON DIAGONAL POINT INCLUSION. |
|---|---|
| Authors: | ALTINTAŞ KAHRİMAN, Elif1 ealtintaskahriman@bartin.edu.tr, BAYAR, Ayşe2 akorkmaz@ogu.edu.tr |
| Source: | Eskişehir Technical University Journal of Science & Technology A - Applied Sciences & Engineering. 2025, Vol. 26 Issue 4, p478-485. 8p. |
| Subjects: | Projective planes, Combinatorial designs & configurations, Quadrilaterals, Geometrical constructions, Finite fields, Algorithms |
| Abstract: | In this study, complete (k, 3) -arcs in the projective plane PG(2,4) that include all vertices of a complete quadrangle are systematically analyzed with respect to the inclusion of diagonal points. A computational algorithm developed in C# was employed to construct and classify such arcs. The results show that the complete quadrangle itself forms a complete (7, 3) -arcs, and exactly 7560 such arcs exist depending on the choice of quadrangle point sets. Furthermore, three distinct types of complete (9, 3) -arcs were identified: 24 arcs containing all four vertices and two diagonals, 48 arcs containing all four vertices and one diagonal point, and 480 arcs with all four vertices and no diagonal points. These findings reveal the combinatorial diversity of arc configurations in finite projective planes and provide new contributions to the classification of arcs. The methodology also demonstrates the effectiveness of algorithmic approaches in investigating geometric structures over finite fields. [ABSTRACT FROM AUTHOR] |
| Copyright of Eskişehir Technical University Journal of Science & Technology A - Applied Sciences & Engineering is the property of Eskisehir Technical University Rector's Office and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 190540021 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: COMPLETE (k,3)-ARCS CONTAINING COMPLETE QUADRANGLE VERTICES IN PG(2,4): STRUCTURAL ANALYSIS BASED ON DIAGONAL POINT INCLUSION. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22ALTINTAŞ+KAHRİMAN%2C+Elif%22">ALTINTAŞ KAHRİMAN, Elif</searchLink><relatesTo>1</relatesTo><i> ealtintaskahriman@bartin.edu.tr</i><br /><searchLink fieldCode="AR" term="%22BAYAR%2C+Ayşe%22">BAYAR, Ayşe</searchLink><relatesTo>2</relatesTo><i> akorkmaz@ogu.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Eskişehir+Technical+University+Journal+of+Science+%26+Technology+A+-+Applied+Sciences+%26+Engineering%22">Eskişehir Technical University Journal of Science & Technology A - Applied Sciences & Engineering</searchLink>. 2025, Vol. 26 Issue 4, p478-485. 8p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Projective+planes%22">Projective planes</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+designs+%26+configurations%22">Combinatorial designs & configurations</searchLink><br /><searchLink fieldCode="DE" term="%22Quadrilaterals%22">Quadrilaterals</searchLink><br /><searchLink fieldCode="DE" term="%22Geometrical+constructions%22">Geometrical constructions</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this study, complete (k, 3) -arcs in the projective plane PG(2,4) that include all vertices of a complete quadrangle are systematically analyzed with respect to the inclusion of diagonal points. A computational algorithm developed in C# was employed to construct and classify such arcs. The results show that the complete quadrangle itself forms a complete (7, 3) -arcs, and exactly 7560 such arcs exist depending on the choice of quadrangle point sets. Furthermore, three distinct types of complete (9, 3) -arcs were identified: 24 arcs containing all four vertices and two diagonals, 48 arcs containing all four vertices and one diagonal point, and 480 arcs with all four vertices and no diagonal points. These findings reveal the combinatorial diversity of arc configurations in finite projective planes and provide new contributions to the classification of arcs. The methodology also demonstrates the effectiveness of algorithmic approaches in investigating geometric structures over finite fields. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Eskişehir Technical University Journal of Science & Technology A - Applied Sciences & Engineering is the property of Eskisehir Technical University Rector's Office and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190540021 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.18038/estubtda.1754684 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 478 Subjects: – SubjectFull: Projective planes Type: general – SubjectFull: Combinatorial designs & configurations Type: general – SubjectFull: Quadrilaterals Type: general – SubjectFull: Geometrical constructions Type: general – SubjectFull: Finite fields Type: general – SubjectFull: Algorithms Type: general Titles: – TitleFull: COMPLETE (k,3)-ARCS CONTAINING COMPLETE QUADRANGLE VERTICES IN PG(2,4): STRUCTURAL ANALYSIS BASED ON DIAGONAL POINT INCLUSION. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: ALTINTAŞ KAHRİMAN, Elif – PersonEntity: Name: NameFull: BAYAR, Ayşe IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 26674211 Numbering: – Type: volume Value: 26 – Type: issue Value: 4 Titles: – TitleFull: Eskişehir Technical University Journal of Science & Technology A - Applied Sciences & Engineering Type: main |
| ResultId | 1 |
