Generalized quadrangles with a regular point and association schemes

AbstractThere is a new method of constructing generalized quadrangles (GQs) which is based on covering of nets; all GQs with a regular point can be represented in this way. Here we first construct from a generalized quadrangle Q with a regular point a four-class association scheme A(Q) called in brief geometric. It is then natural to call pseudo-geometric any association scheme A with the same parameters as A(Q). We use eigenvalue techniques and the above method of construction to give a characterization of pseudo-geometric association schemes which are geometric

Characterization of some 4-gonal configurations of Ahrens–Szekeres type

Motivated by the Ahrens–Szekeres Quadrangles, we shall present a variation of the 4-gonal family method of construction introduced by Kantor in 1980. The relation between generalized quadrangles of order (s, s) and of order (s − 1, s + 1) has been known for a long time. A geometrical description of this interrelation was given by Payne in 1971 and rests on the notion of regular points or of regular lines. In this paper we wish to develop these connections algebraically in the hope of getting more insight into them from the group-theoretical point of view. In this way we are able to characterize two classes of known 4-gonal configurations

Characterization of some 4-gonal configurations of AHRENS-SZEKERES type

Motivated by the Ahrens-Szekeres-Quadrangles I present a variation of the 4-gonal families method of construction introduced by Kantor in 1980. Since a long time it has been known the relation between generalized quadrangles of order (s,s) and of order (s-1,s+1). A geometrical description of this interrelation was given by Payne in 1971 and rests on the notion of regular points or rather of regular lines. In this paper I develop these connections algebraically in the hope of getting more insight into them from the group theoretical point of view. In this way I am able to characterize two classes of known 4-gonal configurations

A non-existence result for finite projective planes in Lenz-Barlotti class I.4

Let Pi be a projective plane of order n in Lenz-Barlotti class I.4, and assume that n is a multiple of 3. Then either n=3 or n is a multiple of 9