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Application of the Young’s Partition Method for Combinatorial Enumeration of Gem Position Isomers of Homo Polysubstituted Linear N-Alkanes (Part I: N Odd)

Robert M. Nemba and Christiane E. Nemba

The formation of cumulative gem homo disubstitutions and trisubstitutions on secondary and primary carbon atoms of a homopolysubstituted linear n-alkane (HPSNA) with the empirical formula CnH2n+2-mXm satisfy three Young’s partitions Eqs. m_ = 32k ±, m+ = 322 k ±, or 2k ± where the positive integer numbers m± ≥ 2 and k± ≥ 0. A generalized combinatorial method derived from these partitions is proposed for counting gem position isomers (GPIs) of such molecular systems having a linear carbon chain length n- (odd) and a degree of substitution m± (odd or even).