Configurations of weighted circles in finite inversive planes (Q1201927)

Let \(I(n)\) be a finite inversive plane of order \(n\). A weighted configuration \(W\) of circles in \(I(n)\) is an incidence structure in \(I(n)\) whose blocks are circles and for each circle is assigned a positive integer called its weight. A weighted configuration \(W=W({\mathcal V},{\mathcal B})\) in \(I(n)\) is an incidence structure with point set \({\mathcal V}\) containing \(v\) points and block set \({\mathcal B}\) consisting of \(b\) circles. The author examines certain combinatorial properties of weighted configurations and gives some conditions under some weighted configurations that can be found in \(M(q)\) (the Miquelian plane where \(q\) is an odd prime power). Moreover the author introduces a special weighted configuration and shows by examples that not all weighted configurations are special. The most interesting are suggestions of ways in which weighted configurations can be developed and generalized.