, Volume 51, Issue 1, pp 239-264
Date: 27 Oct 2012

Enumeration of substitutional isomers with restrictive mutual positions of ligands. II. Counts with restrictions on (sub)symmetry

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The present paper extends our previous discussion of paper I on “Overall Counts”, still focusing on enumerations of substitutional isomers with restrictive positioning of ligands. But now, we address the counts of such isomers with a specified subsymmetry of the symmetry of the parent skeleton. Constrained analogs of Pólya’s cycle index still appear, but now we introduce more powerful technical tools to include subsymmetry-specified generalizations of the cycle index. This involves differential-operator approach for analytically treating newly derived hybrids of the the generalized cycle index and suitable F-polynomials. As a simple illustration of the general mathematical exposition, a specific problems are solved and some tasks for possible further consideration are also stated, where again the Maple symbolic manipulation package proves useful.