Abstract
We consider the following question: Given a family A of sets for which A-blocking sets exist, is it true that any bijection of the set of points which preserves the family of A-blocking sets must preserve A? Using a variet of techniques, we show that the answer is ‘yes’ in many cases, for example, when A is the family of subspaces of fixed dimension in a projective space, lines in an affine plane, or blocks of a symmetric design, but that it is ‘no’ for lines of an arbitrary linear space.
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Work supported by National Research Project on ‘Strutture geometriche, combinatoria loro applicazioni’ of M.P.I. and by G.N.S.A.G.A. of C.N.R.
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Cameron, P.J., Mazzocca, F. Bijections which preserve blocking sets. Geom Dedicata 21, 219–229 (1986). https://doi.org/10.1007/BF00182909
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DOI: https://doi.org/10.1007/BF00182909