Bases of schurian antisymmetric coherent configurations and isomorphism test for schurian tournaments
Presented by Dr. Ilya PONOMARENKO
Type: Oral presentation
Track: Association Schemes
A schurian antisymmetric coherent configuration can be defined as the coherent configuration of a permutation group~$G$ of odd order. It is well-known that for such $G$ one can find a point set the setwise stabilizer of which is trivial, and if the group $G$ is primitive, then also a base of it of size at most~$3$. Both of these results are generalized to the coherent configuration of~$G$. As a byproduct we construct a polynomial-time algorithm for recognizing and isomorphism testing of schurian tournaments (i.e. those tournaments the coherent configurations of which are schurian).