Let (N,Φ) be a finite circular Ferrero pair. We define the disk with center b and radius a,D(a;b) , as D(a;b)={x∈Φ(r)+c∣r≠0,b∈Φ(r)+c,|(Φ(r)+c)∩(Φ(a)+b)|=1}. Using this definition we introduce the concept of interior part of a circle, Φ(a)+b , as the set I(Φ(a)+b)=D(a;b)∖(Φ(a)+b) . Moreover, if BD is the set of all disks, then, in some interesting cases, we show that the incidence structure (N,BD,∈) is actually a balanced incomplete block design and we are able to calculate its parameters depending on |N| and |Φ| .
BIB-designs from circular nearrings
BENINI, Anna;
2013-01-01
Abstract
Let (N,Φ) be a finite circular Ferrero pair. We define the disk with center b and radius a,D(a;b) , as D(a;b)={x∈Φ(r)+c∣r≠0,b∈Φ(r)+c,|(Φ(r)+c)∩(Φ(a)+b)|=1}. Using this definition we introduce the concept of interior part of a circle, Φ(a)+b , as the set I(Φ(a)+b)=D(a;b)∖(Φ(a)+b) . Moreover, if BD is the set of all disks, then, in some interesting cases, we show that the incidence structure (N,BD,∈) is actually a balanced incomplete block design and we are able to calculate its parameters depending on |N| and |Φ| .File in questo prodotto:
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