Abstract
A characterization of sharply n-transitive sets of permutations or of mappings is given by means of Buekenhout diagrams. As a by-product, a characterization is obtained in the same style for finite Minkowski and Laguerre planes. Two preliminary results are used to obtain these diagram-theoretic descriptions. One of them gives us a characterization of the complement of a square lattice graph by means of the nonexistence of certain configurations. The other one states that every net of degree s + 1 with s + 2 points on each line is embeddable in a projective plane of order s + 2. This latter result is exploited to get control over the geometries appearing as rank 2 residues on top in the diagrams we consider. Next, we can use the earlier result to obtain the information we need on the point-graphs of the geometries we want to describe.
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Communicated by D. Jungnickel
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Pasini, A. Diagram geometries for sharply n-transitive sets of permutations or of mappings. Des Codes Crypt 1, 275–297 (1991). https://doi.org/10.1007/BF00124604
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DOI: https://doi.org/10.1007/BF00124604