Why Enumerate

3 Why Enumerate . - Clearly enumeration has played an important role in the history of chemistry. But does it still Are the noted enumerations just historical anachronisms Is enumeration irrelevant for modem interests in quantitative descriptions of different substances Indeed in all the areas we have noted, one may indeed argue that enumeration is but a first step towards a more comprehensive characterization and undertaking. Combinatorial formulae often merely identify two different enumerations to have equal values, with one of the enumerations being the easier to perform. We may note for instance that isomer enumeration in Polya theory identifies this enumeration to that of the enumeration of certain equivalence classes of functions. With the counts for two different sets of objects being equal, there often is a natural bijection i.e. a one-to-one correspondence) between the two sets, so that the objects of one set may be used to represent (or even name) those of the other. Thence for the case of chemical isomers again, the mathematical set of objects offers a nomenclature for the isomers. Conversely too, granted a nomenclature, a possibility for enumeration is offered one seeks to enumerate the names (which presumably exhibit some systematic structure). In some sense then a sensible nomenclature and enumera- 

In a number of contexts it seems that transformed enumerations are actually of more central interest. In particular rather than the numbers jv of some objects of a size N, interest may focus on an associated generating function 

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But excuse me, Ghichikov intervened at last, astonished at this flood of seemingly endless eloquence, why enumerate all their qualities There s no sense in it, they are all dead folk. You might as well prop a fence with a dead body, as the proverb has it. ... 

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