  We show that many theorems which assert that two kinds of partitions of the
same integer $n$ are equinumerous are actually special cases of a much stronger
form of equality. We show that in fact there correspond partition statistics
$X$ and $Y$ that have identical distribution functions. The method is an
extension of the principle of sieve-equivalence, and it yields simple criteria
under which we can infer this identity of distribution functions.

Combinatorics