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ON GENERATING FUNCTIONS IN THE THEORY OF NUMBERS. 
a variety of arithmetical correspondences which, as before remarked, is absolutely 
limitless. 
The theory, moreover, includes an exhaustive Theory of Permutations, and gives in 
every case the true condensed Generating Functions, Its importance in the General 
Theory of Determinants has been touched upon. 
In conclusion, the paper will have achieved its object if it is successful in indicating 
the arithmetical and algebraical power of the main theorem considered. 
