If S is a set of points of a projective plane, then by L_i(S) we denote the set of all lines intersecting S in exactly i ponts. By i-dual set of S we mean the dual set of L_i(S) in the dual plane. In order to discover new examples of minimal blocking sets of a projective plane, we propose to look at the i-dual set of a minimal blocking set. As a matter of fact, in this note, we show that sometimes it happens that such a dual set is a minimal blocking set too. In particular, we suggest the notion of vector of a set (and also of vector of a point) and we present some examples of minimal blocking sets whose i-dual sets are minimal blocking sets of the same vector.

Some remarks on minimal blocking sets

INNAMORATI, STEFANO;ZUANNI, FULVIO
2003

Abstract

If S is a set of points of a projective plane, then by L_i(S) we denote the set of all lines intersecting S in exactly i ponts. By i-dual set of S we mean the dual set of L_i(S) in the dual plane. In order to discover new examples of minimal blocking sets of a projective plane, we propose to look at the i-dual set of a minimal blocking set. As a matter of fact, in this note, we show that sometimes it happens that such a dual set is a minimal blocking set too. In particular, we suggest the notion of vector of a set (and also of vector of a point) and we present some examples of minimal blocking sets whose i-dual sets are minimal blocking sets of the same vector.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/7228
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