match89n2

Abstract

The mathematical properties of isomers numbers of substituted $C_{2 v}$ -based compounds presented in this paper includes : -(1) the formulation of 4-dimensional permutomers count vectors $P C V = (N_{E}, N_{C_{2}}, N_{σ_{v_{1}}}, N_{σ_{v_{2}}})$ and 5-dimensional itemized isomers count vectors IICV= $a_{c_{1}}, a_{c_{2}}, a_{c_{s}}, a_{c_{s}^{'}}, a_{c_{2 v}}$ which satisfy the dot product PCV = $I I C V \times W_{C_{2 v}}$ . (2)- The expansion of this equation to obtain the denumerants of type $N_{g_{i} ϵ C_{2 v}} = \sum_{g_{i} ϵ C_{2 v}} a_{G_{j} ϵ C_{2 v}} W_{G_{j}}, g_{i}$ mapping permutomers numbers as sum of symmetry itemized isomers numbers $a_{G_{j} ϵ C_{2 v}}$ scaled by $W_{G_{j}}, g_{i}$ the markaracters of $C_{2 v}$ . (3)-The collection of 4 and 5 entries $P C V_{s}$ and $I I C V_{s}$ generating respectively, permutomers count matrices $(P C M_{s})$ and itemized isomers count matrices $(I I C M_{s})$ that construct two associated vector spaces of isomers numbers for such series of molecules.