BASES OF SCHURIAN ANTISYMMETRIC COHERENT CONFIGURATIONS AND AN ISOMORPHISM TEST FOR SCHURIAN TOURNAMENTS

摘要

It is known that for any permutation group G of odd order there exists a subset of the permuted set whose stabilizer in G is trivial, and if G is primitive, then there also exists a base of size at most 3. These results are generalized to the coherent configuration of G, which in this case is schurian and antisymmetric. This enables us to construct a polynomial-time algorithm for recognizing and isomorphism testing of schurian tournaments (i.e., arc-colored tournaments whose coherent configurations are schurian). Bibliography: 24 titles.