A mathematical characterization of the groups of substitution isomerism of the linear alkanes

In this paper, a mathematical characterization of Lunn–Senior’s groups of univalent substitution isomerism of the linear alkanes, under some natural assumptions that reflect their common properties, is given. For each linear alkane, the number of its monosubstitution derivatives, its di-substitution derivatives, and its tri-substitution derivatives as linear, quadratic, and cubic polynomial expressions, respectively, in their number, is obtained. In principle, the number of derivatives of a given linear alkane with any particular composition can be established. The same explicit expressions for the case of k-substitution homogeneous derivatives of the linear alkanes are obtained by Balasubramanian (Theoret. Chim. Acta (Berl.) 51:37, 1979).