Abstract
Finding the number of isomers of compounds with a given molecular geometry or the number of chain isomers of an alkane or alkyl group is analogous to finding the number of ways of colouring the vertices of a polyhedron (or the beads in a necklace) with a given number of colours. Pólya’s enumeration theorem (PET), which involves the concept of permutation groups and cycle indices, is a powerful method for this purpose. The present article attempts to explain the ‘permutation group’ and ‘cycle index’ of a permutation from an elementary level of understanding and shows how PET works in finding the number of chain isomers of alkanes and alkanols and geometrical isomers of tetrahedral Mabcd, Mab3, Ma2b2 and octahedral Mabcdef, Mab5, Ma2b4 and Ma3b3 types of molecules.
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Bankim Chandra Ghosh is an Assistant Professor of chemistry at Government General Degree College–Singur, West Bengal. His current research interest is graph and group theoretical calculation on some carbon nanomaterials.
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Ghosh, B.C. Permutation Groups and Enumeration of Isomers. Reson 28, 1401–1415 (2023). https://doi.org/10.1007/s12045-023-1676-3
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DOI: https://doi.org/10.1007/s12045-023-1676-3