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Title:
Vector Spaces of Permutomers and Symmetry Itemized Isomers Numbers for Substituted \(C_{2V}\)-Based Compounds. I
Authors:
Robert Martin Nemba
doi:
Volume
89
Issue
2
Year
2023
Pages
287-300
Abstract The mathematical properties of isomers numbers of substituted \(C_{2v}\)-based compounds presented in this paper includes : -(1) the formulation of 4-dimensional permutomers count vectors \(PCV =( N_{E},N_{C_{2}},N_{\sigma_{v_{1}}},N_{\sigma_{v_{2}}})\) and 5-dimensional itemized isomers count vectors IICV=\(a_{c_{1}},a_{c_{2}},a_{c_{s}},a_{c'_s},a_{c_{2v}}\) which satisfy the dot product PCV =\(IICV\times W_{C_{2v}}\) . (2)- The expansion of this equation to obtain the denumerants of type \(N_{g_{i}\epsilon C_{2v}}=\sum_{g_{i}\epsilon C_{2v}} a_{G_{j}\epsilon C_{2v}}W_{G_j},{g_i}\) mapping permutomers numbers as sum of symmetry itemized isomers numbers \(a_{G_{j}\epsilon C_{2v}}\) scaled by \(W_{G_j},{g_i}\) the markaracters of \(C_{2v}\). (3)-The collection of 4 and 5 entries \(PCV_s\) and \(IICV_s\) generating respectively, permutomers count matrices \((PCM_s)\) and itemized isomers count matrices \((IICM_s)\) that construct two associated vector spaces of isomers numbers for such series of molecules.

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