We present three constructions which transform some symmetric configurations $\cal{K}$ of type $n_k$ into new symmetric configurations of types $(n + 1)_k$, or $n_{k−1}$, or $((\lambda − 1) \mu )_{k−1}$ if $n = \lambda \mu$. Applying them to Desarguesian elliptic semiplanes, an infinite family of new configurations comes into being, whose types fill large gaps in the parameter spectrum of symmetric configurations.

Deletions, Extensions and Reductions of Elliptic Semiplanes

ABREU, Marien;FUNK, Martin;LABBATE, Domenico;
2010

Abstract

We present three constructions which transform some symmetric configurations $\cal{K}$ of type $n_k$ into new symmetric configurations of types $(n + 1)_k$, or $n_{k−1}$, or $((\lambda − 1) \mu )_{k−1}$ if $n = \lambda \mu$. Applying them to Desarguesian elliptic semiplanes, an infinite family of new configurations comes into being, whose types fill large gaps in the parameter spectrum of symmetric configurations.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/9233
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