We show that the maximum size of a geometry of rank n excluding the (q + 2)-point line, the 3-wheel W_3, and the 3-whirl W^3 as minor is (n - 1)q + 1, and geometries of maximum size are parallel connections of (q + 1)-point lines. We show that the maximum size of a geometry of rank n excluding the 5-point line, the 4-wheel W_4, and the 4-whirl W^4 as minors is 6n - 5, for n ≥ 3. Examples of geometries having rank n and size 6n - 5 include parallel connections of the geometries V_19 and PG(2,3).
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc330849 |
| Date | 08 1900 |
| Creators | Hipp, James W. (James William), 1956- |
| Contributors | Kung, Joseph P. S., Brand, Neal E., Lewis, Paul Weldon, Jacob, Roy Thomas |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 68 leaves : ill., Text |
| Rights | Public, Hipp, James W. (James William), 1956-, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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