Geodesic
Symmetric multiplicative statistics
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 280-289

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The author constructs the family of multiplicative statistics on integer partitions that are symmetric in the sense that the statistics is invariant under conjunction of Young diagram. It is shown that all symmetric multiplicative statistics lie in this family. A limit shape of Young diagrams under these statistics is found. 
@article{ZNSL_1997_240_a17,
     author = {Yu. V. Yakubovich},
     title = {Symmetric multiplicative statistics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {280--289},
     publisher = {mathdoc},
     volume = {240},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a17/}
}
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Yu. V. Yakubovich. Symmetric multiplicative statistics. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 280-289. http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a17/