Pairwise transitive 2-designs

Alice Devillers; Cheryl E. Praeger

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arXiv · 1405.3030

Pairwise transitive 2-designs

Alice Devillers·Cheryl E. Praeger

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Abstract

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.

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Alice Devillers, Cheryl E. Praeger. 2014-05-13. Pairwise transitive 2-designs. https://arxiv.org/abs/1405.3030

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