Philosophiae Doctor - PhD / A tactical con guration consists of a nite set V of points, a nite set B of
blocks and an incidence relation between them, so that all blocks are incident
with the same number k points, and all points are incident with the same
number r of blocks (See [14] for example ). If v := jV j and b := jBj; then
v; k; b; r are known as the parameters of the con guration. Counting incident
point-block pairs, one sees that vr = bk:
In this thesis, we generalize tactical con gurations on Steiner triple systems
obtained from projective geometry. Our objects are subgeometries as blocks.
These subgeometries are collected into systems and we study them as designs
and graphs. Considered recursively is a further tactical con guration on some
of the designs obtained and in what follows, we obtain similar structures as
the Steiner triple systems from projective geometry. We also study these
subgeometries as factorizations and examine the automorphism group of the
new structures.
These tactical con gurations at rst sight do not form interesting structures.
However, as will be shown, they o er some level of intriguing symmetries.
It will be shown that they inherit the automorphism group of the
parent geometry.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uwc/oai:etd.uwc.ac.za:11394/6735 |
| Date | January 2018 |
| Creators | Vodah, Sunday |
| Contributors | Mwambene, Eric |
| Publisher | University of the Western Cape |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Rights | University of the Western Cape |
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