Some topological and combinatorial properties ofc-component (c + 4)-phase multisystem nets

Multisystem nets are topological analogs of real and potentially real phase diagrams which can be constructed given only the chemography of phases of interest. Combinatorial analysis of c-component (c + 4)-phase multisystems suggests the existence of (c + 4)!/2] 2^{(c +4)} – 2 (c + 4)] distinct nets. (c + 4)-phase multisystem nets are characterized by three different invariant point stability levels, four different reaction stability levels, and three invariant points along each univariant reaction. Invariant points at the intermediate stability level occur in two disjoint networks. Unlike (c + 3)-phase multisystems, in which all nets are related by transposition, (c + 4)-phase nets form distinct equivalence classes under transposition based on identities of those invariant points at the intermediate stability level. A position matrix is introduced to denote adjacency/connectivity relationships, and a relationship is suggested between the number of nets in each equivalence class under transposition and the number of ways of assigning stability levels to invariant points of an arbitrary position matrix.