Algebraic determination of generating functions for coordination sequences in crystal structures.
Given a connected crystalline structure, the set of paths and cycles of the quotient graph of its bond net is embedded into a commutative ring structure. Multiplication combines walks to build up geodesics of the net whereas addition stands symbolically for enumerating a collection of walks. Topological criteria are used to define zero divisors which enable the development of an algebraic generator into a combination of geodesics that are in a one-to-one correspondence with the vertices of the net. A ring mapping gives the generating function of the coordination sequence in the net.
Eon
Jean Guillaume
JG
Instituto de Química, Universidade Federal do Rio de Janeiro, A-632, Cidade Universitária, 21945-970 Ilha do Fundão, Rio de Janeiro, Brazil. jgeon@iq.ufrj.br