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

DOI: 10.1007/s10910-012-0076-9

Cite this article as:
Rosenfeld, V.R. & Klein, D.J. J Math Chem (2013) 51: 239. doi:10.1007/s10910-012-0076-9


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.


EnumerationSubstitutional isomersRestrictive substitutionSymmetry-restrictiveF-polynomials

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

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