Can anyone tell me the purpose and/or derivation of the "Cauchy number" of a permutation of a symmetric group, REA GRE Practice Test 3, Prob. #62? Cauchy made a lot of numbers.... (Overacheiver. ) The only one I can find anywhere is in physics, although obviously I'm sure this one is closely related to his theorem about orders of groups.

(Paraphrased) "If Sn is split into n disjoint subgroups of orders a1, a2...an, the Cauchy number is Sum[i=1 to n] {ai-1}.

This is all the explanation given. The computation is easy, but I don't understand why I'm doing it. It's not describing the number of generators according to the permutation, is it?

Thanks!