ALGEBRAIC DESCRIPTION OF COORDINATION SEQUENCES AND EXACT TOPOLOGICALDENSITIES FOR ZEOLITES

Coordination sequences (CS) have been calculated for all approved zeol ite topologies, all dense SiO2 polymorphs and 16 selected non-tetrahed ral structures and the algebraic structure of these CS's has been anal yzed. Two algebraic descriptions of coordination sequences are present ed. One description uses periodic sets of quadratic equations and is a lready established in the Literature. The second description employs g enerating functions, which are well known in combinatorics but are use d here for the first time in connection with coordination sequences. T he algebraic analysis based on generating functions turns out to be mo re powerful than the other approach. Based on the algebraic analyses, exact topological densities are derived and tabulated for all the stru ctures investigated. In addition, 'n-dimensional sodalite' is observed to have an especially simple n-dimensional graph.