Efficient algorithms to enumerate isomers and diamutamers with more than one type of substituent

In this paper we describe numeric as well as symbolic algorithms for the enumeration of substitutional isomers with an unlimited number of different achiral substituents. We consider three different scenarios: first, the enumeration of diamutamers with a given set of ligand types and ligand multiplicity, second, the enumeration of diamutamer libraries with a given ligand assortment pattern, and, third, the enumerations of libraries with diamutamers exhibiting a limited number of ligands.