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Construction of Arcs (k, 5) - at the level of Dizark PG (2,9) (*) | ||
| Journal of Education and Science | ||
| Article 22, Volume 22, Issue 1, 2009, Pages 133-150 PDF (0 K) | ||
| DOI: 10.33899/edusj.2009.57419 | ||
| Authors | ||
| Abdulkhalik Yaseen* ; Farah Hasim Mohammed | ||
| Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq | ||
| Abstract | ||
| Abstract 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 . | ||
| Keywords | ||
| Construction; Arcs(k; 5); Dizark level PG(2; 9) | ||
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