Algebraic description of coordination sequences and exact topological densities for zeolites

Coordination sequences (CS) have been calculated for all approved zeolite topologies, all dense SiO2 polymorphs and 16 selected non-tetrahedral structures and the algebraic structure of these CS's has been analyzed. Two algebraic descriptions of coordination sequences are presented. One description uses periodic sets of quadratic equations and is already established in the Literature. The second description employs generating functions, which are well known in combinatorics but are used here for the first time in connection with coordination sequences. The algebraic analysis based on generating functions turns out to be more powerful than the other approach. Based on the algebraic analyses, exact topological densities are derived and tabulated for all the structures investigated. In addition, 'n-dimensional sodalite' is observed to have an especially simple n-dimensional graph.