Extending Symmetric Variable-Pair Transitivities Using State-Space Transformations

Two-cofactor relations and their associated symmetry types have been studied for many years. While ordinary symmetries are simply transitive permitting them to be combined into clusters of variables, other types of symmetries have more complex transitivities. This paper shows how to convert the various types of symmetry into ordinary symmetries using state-space transformations. This permits the simple transitivity of ordinary symmetry to be extended to virtually any type of symmetry.