ON A METHOD OF CONSTRUCTION OF PARTIAL GEOMETRIES AND PARTIAL BOLYAI-LOBACHEVSKY PLANES.
Technical rept. no. 5
MICHIGAN STATE UNIV EAST LANSING
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The concept of partial geometries was introduced by R. C. Bose Strongly regular graphs, partial geometries and partially balanced block designs. The partial BolyaiLobachevsky planes were introduced by L. M. Graves A finite Bolyai-Lobachevsky plane. Graves states, It would be interesting to know methods for constructing additional examples of finite B-L planes, and to learn the limitations on the number n of points on a line and the number nu of lines on a point. The purpose of this paper is to point out that any projective plane of even order, say 2h possessing an oval, set of points no three on one line, of 2h2 points generates two disjoint partial geometries. The dual of one of these partial geometries obtained by interchanging the roles of the points and the lines forms a B-L plane. Author