Geodesic
Identically Distributed Pairs of Partition Statistics
Séminaire lotharingien de combinatoire, Tome 44 (2000-2001)

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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. 

@article{SLC_2000-2001_44_a2,
     author = {Herbert S. Wilf},
     title = {Identically {Distributed} {Pairs} of {Partition} {Statistics}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {44},
     year = {2000-2001},
     url = {http://geodesic.mathdoc.fr/item/SLC_2000-2001_44_a2/}
}
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%0 Journal Article
%A Herbert S. Wilf
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%J Séminaire lotharingien de combinatoire
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%U http://geodesic.mathdoc.fr/item/SLC_2000-2001_44_a2/
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Herbert S. Wilf. Identically Distributed Pairs of Partition Statistics. Séminaire lotharingien de combinatoire, Tome 44 (2000-2001). http://geodesic.mathdoc.fr/item/SLC_2000-2001_44_a2/