Thesis (M.C.S.)--Carleton University, 2004. / Includes bibliographical references (p. 27-29). Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Hong Kong, 1997. / Includes bibliographical references (leaf 98-103).

Thesis (M.S.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaf 34).

No description available.

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.

published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 132-137. / Ph.D.

No description available.

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).

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / Vita. / Bibliography: leaves 132-133. / by Nguyen Quang Hien. / Ph.D.