Abstract
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 language | English |
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Pages (from-to) | 203-221 |
Number of pages | 19 |
Journal | Designs, Codes, and Cryptography |
Volume | 84 |
Issue number | 1-2 |
DOIs | |
State | Published - 1 Jul 2017 |
Keywords
- 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