On the existence of block-transitive combinatorial designs

Details On the existence of block-transitive combinatorial designs On the existence of block-transitive combinatorial designs

2010-03-09

arxiv.org/abs/1003.1879v1

Mathematics

Combinatorics

9 pages; to appear in "Discrete Mathematics and Theoretical Computer Science (DMTCS)"

Scientific paper

Block-transitive Steiner $t$-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory, and cryptography. The main result of the paper settles an important open question: There exist no non-trivial examples with $t=7$ (or larger). The proof is based on the classification of the finite 3-homogeneous permutation groups, itself relying on the finite simple group classification.

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