Abstract
The set of coset representations, CR's, of a group G, {G(/G1), G(/G2), ..., G(/Gs)}, where G1 = {I}, Gs = G, the marks, mij of subgroup Gj on a given G(/Gi), 1 ≤ i ≤ s, and the subduction of G(/Gi) by Gj, j ≤ i, G(/Gi) ↓ Gj, are essential tools for the enumeration of stereoisomers and their classification according to their subgroup symmetry (Fujita, S. Symmetry and Combinatorial Enumeration in Chemistry; Springer−Verlag: Berlin, 1991). In this paper, each G(/Gi) is modeled by a set of colored equivalent configurations (called homomers), ℋ = {h1, h2, ..., hr}, r = |G|/|Gi|, such that a given homomer, hk, remains invariant only under all g ∈ Gi, where g is an element of symmetry. The resulting homomers generate the corresponding set of marks almost by inspection. The symmetry relations among a set ℋ can be conveniently stored in a Cayley-like diagram (Chartrand, G. Graphs as Mathematical Models; Prindle, Weber and Schmidt Incorporated: Boston, MA, 1977; Chapter 10), which is a complete digraph on r vertic...
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