The number of permutational isomers (or of elements in a combinatorial library that arises from a central molecule with equal active sites via reactions with building blocks) can be obtained as follows:

Number the sites of the skeleton (or the active sites of the central molecule) from 1 to n, and enter a vector of generators of the symmetry group of the skeleton (central molecule) in list notation (for example, if n=4, the following vector that generates the full symmetric group: [[2,1,3,4],[2,3,4,1]])

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Enter the number of different ligands (building blocks) you want to allow:

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Start the the computation using the start button, in due course you will obtain the total number of such permutational isomers (molecules in the library).

The generating function for the numbers of permutational isomers (or the generating function for the elements of a combinatorial library of molecules) by weight

Number the sites of the skeleton (or the active sites of the central molecule) from 1 to n, and enter a vector of generators of the symmetry group of the skeleton in list notation. (for example, if n=4: [[2,1,3,4],[2,3,4,1]])

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Enter the number of different ligands you want to allow:

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Please start the the computation using the start button. You will in due course obtain the so-called group-reduction-function which is a sum of expressions like this 4 [0,0,2,3,0]. The given summand 4[0,0,2,3,0] means that there are exactly 4 permutational isomers (or molecules in the combinatorial library) that contain 2 ligands of the third and 3 ligands of the fourth kind (if you entered 5 as the intended number of ligands)