We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc277894 |
| Date | 08 1900 |
| Creators | Yoon, Young-jin |
| Contributors | Kung, Joseph P. S., Jackson, Steve, 1957-, Zamboni, Luca Quardo, 1962-, Jacob, Roy Thomas, Brand, Neal E. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 44 leaves: ill., Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Yoon, Young-jin |
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