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

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

2011-08-29

arxiv.org/abs/1108.5645v1

Mathematics

Combinatorics

30 pages

Scientific paper

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).

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