Identically Distributed Pairs of Partition Statistics

Details Identically Distributed Pairs of Partition Statistics Identically Distributed Pairs of Partition Statistics

2000-04-28

arxiv.org/abs/math/0004180v1

Mathematics

Combinatorics

Scientific paper

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.

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