Journal of Mathematical Chemistry

, Volume 51, Issue 1, pp 239–264

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

Original Paper


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.


Enumeration Substitutional isomers Restrictive substitution Symmetry-restrictive F-polynomials 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematical Chemistry Group, Department of Marine SciencesTexas A&M University at GalvestonGalvestonUSA

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