Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*)
Abstract<br /> A (k,n) – arc in the finite projective PG(2,q) is defined to be the set K which is composed of k points such that there is a line passes through n points but no line can pass through more than n points. A (k,n) – arc is called complete if there is no (k+1,n) – arc containing it....
| Main Authors: | , |
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| Format: | Article |
| Language: | Arabic |
| Published: |
College of Education for Pure Sciences
2009-03-01
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| Series: | مجلة التربية والعلم |
| Subjects: | |
| Online Access: | https://edusj.mosuljournals.com/article_57419_4519168608c55a7cb8a82ab330730b4f.pdf |
| _version_ | 1819211618993569792 |
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| author | Abdulkhalik Yaseen Farah Mohammed |
| author_facet | Abdulkhalik Yaseen Farah Mohammed |
| author_sort | Abdulkhalik Yaseen |
| collection | DOAJ |
| description | Abstract<br /> A (k,n) – arc in the finite projective PG(2,q) is defined to be the set K which is composed of k points such that there is a line passes through n points but no line can pass through more than n points. A (k,n) – arc is called complete if there is no (k+1,n) – arc containing it. In this research we have constructed and classified all the projectively distinct (k,5) – arcs for k = 7, 8, 9 in the projective planes PG(2,9). We proved that (k,5) – arcs are not complete in the projective plane PG(2, 9) for 5 k 25. We contructed and classified the (13,5) – arcs in the projective plane PG(2,9) where all of these arcs containing a conic by using a computer program . |
| first_indexed | 2024-12-23T06:29:57Z |
| format | Article |
| id | doaj.art-3940f86da82740f9a23258dd581ccaf0 |
| institution | Directory Open Access Journal |
| issn | 1812-125X 2664-2530 |
| language | Arabic |
| last_indexed | 2024-12-23T06:29:57Z |
| publishDate | 2009-03-01 |
| publisher | College of Education for Pure Sciences |
| record_format | Article |
| series | مجلة التربية والعلم |
| spelling | doaj.art-3940f86da82740f9a23258dd581ccaf02022-12-21T17:56:58ZaraCollege of Education for Pure Sciencesمجلة التربية والعلم1812-125X2664-25302009-03-0122113315010.33899/edusj.2009.5741957419Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*)Abdulkhalik Yaseen0Farah Mohammed1Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, IraqDepartment of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, IraqAbstract<br /> A (k,n) – arc in the finite projective PG(2,q) is defined to be the set K which is composed of k points such that there is a line passes through n points but no line can pass through more than n points. A (k,n) – arc is called complete if there is no (k+1,n) – arc containing it. In this research we have constructed and classified all the projectively distinct (k,5) – arcs for k = 7, 8, 9 in the projective planes PG(2,9). We proved that (k,5) – arcs are not complete in the projective plane PG(2, 9) for 5 k 25. We contructed and classified the (13,5) – arcs in the projective plane PG(2,9) where all of these arcs containing a conic by using a computer program .https://edusj.mosuljournals.com/article_57419_4519168608c55a7cb8a82ab330730b4f.pdfconstructionarcs(k5)dizark level pg(29) |
| spellingShingle | Abdulkhalik Yaseen Farah Mohammed Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*) مجلة التربية والعلم construction arcs(k 5) dizark level pg(2 9) |
| title | Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*) |
| title_full | Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*) |
| title_fullStr | Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*) |
| title_full_unstemmed | Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*) |
| title_short | Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*) |
| title_sort | construction of arcs k 5 at the level of dizark pg 2 9 |
| topic | construction arcs(k 5) dizark level pg(2 9) |
| url | https://edusj.mosuljournals.com/article_57419_4519168608c55a7cb8a82ab330730b4f.pdf |
| work_keys_str_mv | AT abdulkhalikyaseen constructionofarcsk5atthelevelofdizarkpg29 AT farahmohammed constructionofarcsk5atthelevelofdizarkpg29 |