The main theme of this thesis is to classify subsets in PG(2, 13) of k elements where no three are collinear. Such sets are called k-arcs. In particular, we are interested in the values of k for which the k-arc is complete. Chapter 1 is devoted to basic definitions of projective spaces of n dimensions, subspaces and the fundamental theorem of projective geometry. Chapter 2 is a preliminary to the main task. It contains the construction of PG(1, q) and the classification of all subsets of PG(1, 13). Chapter 3 is devoted to the construction of PG(2, q), derivation of some general equations and a few small results used in the plane. Chapter 4 is the main one and it contains the complete classification of k-arcs in PG(2, 13). In Chapter 5 the work is extended to projective spaces of order 17 and 19 as a test for the computer programs. Finally, there is a list of the programs used as well as tables of the points of the planes discussed throughout the work.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:618719 |
| Date | January 1993 |
| Creators | Ali, Abbas Husain |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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