Configurations of weighted circles in finite inversive planes

A weighted configurationW of circles in I(n), a finite inversive plane of ordern, is an incidence structure in I(n) whose blocks are circles, to each of which is assigned a positive integer called itsweight. W must satisfy the condition that the sum of the weights of the circles meeting at any point must ben + 1. Some properties ofW, particularly whenI(n) is the Miquelian plane M(q), are developed. It is shown that any spreadS in PG(3,q) induces weighted configurations {W(S)} in M(q), calledspecial. Thus properties ofS may be derived from properties ofThis research was supported by NSERC Grant No. A4827 (Canada). The paper was written while the author held a visiting apointment at Clemson University, Clemson, South Carolina.