Investigation Of Coherent Configurations For N-dimensional Cube

Association scheme theory is an important branch of algebraic combinatorics.Therefore,The construction of a new association scheme is an important part of the research.Higman generalized the concept of association scheme and got the concept of coherent configuration.The orbits of arbitrary permutation group acting on the ? × ? is formed into a association scheme or coherent configuration.Each orbit is recorded as an associate class or a basic relation,and a new association scheme can be obtained by combining the basic relation of the coherent configuration.In this paper,we use the method of constructing the association scheme to study from the following sections.The introduction mainly introduce the research background and current situation of the association scheme and coherent configurations.The first chapter mainly introduce the definition of association scheme,coherent configuration.The second chapter mainly study the structure of 4-dimensional cube association scheme and coherent configuration,Therefore,we get a new association scheme by combining the association class or basic relation.The third chapter mainly study the structure of 5-dimensional cube coherent configuration,Therefore,we get a new association scheme by combining the basic relation.