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## Abstract

© 2015 Elsevier Inc. We classify the pairwise transitive 2-designs, that is, 2-designs such that a group of automorphisms is transitive on the following five sets of ordered pairs: point-pairs, incident point-block pairs, non-incident point-block pairs, intersecting block-pairs and non-intersecting block-pairs. These 2-designs fall into two classes: the symmetric ones and the quasisymmetric ones. The symmetric examples include the symmetric designs from projective geometry, the 11-point biplane, the Higman-Sims design, and designs of points and quadratic forms on symplectic spaces. The quasisymmetric examples arise from affine geometry and the point-line geometry of projective spaces, as well as several sporadic examples.

Original language | English |
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Pages (from-to) | 246-270 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 132 |

DOIs | |

Publication status | Published - May 2015 |

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## Projects

- 1 Finished