Research On Coherent Configuration With Two Fibers

The study of association scheme begins with thinking of group classification. Withthe help of classification of association scheme, we can get group classification. In order toget accurately classification of association scheme, we need to construct diferent types ofassociation scheme. Therefore, the research of constructing methods has already becomea major researching content of association scheme.As the promotion of association scheme, coherent configuration which has a closelink with association scheme is often used to construct association scheme. Also commonlyused to construct association scheme. For a coherent configuration, there are two methodsto construct association scheme. This thesis researches the coherent configuration withtwo fibers and constructing association scheme by one of the methods.In this thesis, it is firstly proved that at least nine necessary conditions must be sat-isfied when a coherent configuration with two fibers is merged into construct associationschemes. Then consider the action of Automorphism group of Clebsch graph on the set-s of quadrangle, edge, skew systems of quadrangles, we can get a coherent configurationwith three fibers. Split the coherent configuration into three coherent configurations whichare all coherent configuration with two fibers. Consider the three examples of coherentconfiguration with two fibers, apply the nine necessary condition which we have proofedand with the help of computers, we get the main results:By merging the relation of the first coherent configuration, we get two associationschemes of rank6, three association schemes of rank5, two association schemes of rank4, three association schemes of rank3, we get in all ten association schemes.By merging the relation of the second coherent configuration, we get one associationschemes of rank5, two association schemes of rank4, two association schemes of rank3,we get in all five association schemes.By merging the relation of the third coherent configuration, we get one associationschemes of rank4, two association schemes of rank3, we get in all three associationschemes.