ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 05B05 Pavčević, Mario-Osvin, University of Zagreb, Croatia On two series of symmetric designs The Menon series of symmetric designs has parameters (4u^{2}, 2u^{2}−u, u^{2}−u). There are two nice tactical decompositions of the sets of points and blocks but none of them could be extended to a general construction of designs. In the case of Wilson-Brouwer series, a general construction for a subseries with parameters (2q^{2} + 2q + 1, q^{2}, 1/2q(q − 1)), q being an odd prime, has been found. It is constructed using a tactical decomposition induced by the action of the cyclic group Z_{q} having 2q + 1 fixed points. This construction leads to many nonisomorphic designs for each admissable q. The second case is a joint work with E. Spence.