Michael Huber - On the existence of block-transitive combinatorial designs

dmtcs:516 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 1 - https://doi.org/10.46298/dmtcs.516
On the existence of block-transitive combinatorial designsArticle

Authors: Michael Huber 1

  • 1 Wilhelm-Schickard-Institut für Informatik [Tübingen]

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.

Volume: Vol. 12 no. 1
Section: Combinatorics
Published on: January 1, 2010
Imported on: March 26, 2015
Keywords: Combinatorial design,block-transitive group of automorphisms,3-homogeneous permutation group,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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