A non-Schurian coherent configuration on 14 points exists

Mikhail Klin, Matan Ziv-Av

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


For a few decades the smallest known non-Schurian coherent configuration was the association scheme on 15 points, coming from a doubly regular tournament. Last year the second author, using a computer, enumerated all coherent configurations of order up to 15. A consequence of the enumeration is that all coherent configurations up to 13 points are Schurian and a unique non-Schurian rank 11 coherent configuration of order 14 exists. This coherent configuration has two fibers of sizes 6 and 8, and an automorphism group of order 24 isomorphic to SL(2, 3). We provide a computer free interpretation of this new object, relying on some simple interplay between group theoretical and combinatorial arguments.

Original languageEnglish
Pages (from-to)203-221
Number of pages19
JournalDesigns, Codes, and Cryptography
Issue number1-2
StatePublished - 1 Jul 2017


  • Association scheme
  • Automorphism group
  • Cayley graph
  • Centralizer algebra
  • Coherent configuration
  • Quaternion group

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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