Bases of schurian antisymmetric coherent configurations and isomorphism test for schurian tournaments

TL;DR

This paper generalizes known permutation group results to schurian antisymmetric coherent configurations, enabling polynomial-time algorithms for recognizing and testing isomorphism of schurian tournaments.

Contribution

It extends classical permutation group theorems to coherent configurations, leading to efficient isomorphism testing algorithms for schurian tournaments.

Findings

Generalized base size results to coherent configurations

Developed polynomial-time isomorphism testing algorithm for schurian tournaments

Provided structural insights into schurian antisymmetric coherent configurations

Abstract

It is known that for any permutation group $G$ of odd order one can find a subset of the permuted set whose stabilizer in $G$ is trivial, and if $G$ is primitive, then also a base of size at most 3. Both of these results are generalized to the coherent configuration of $G$ (that is in this case a schurian antisymmetric coherent configuration). This enables us to construct a polynomial-time algorithm for recognizing and isomorphism testing of schurian tournaments (i.e. arc colored tournaments the coherent configurations of which are schurian).