Geodesic
Hoeffding spaces and Specht modules
ESAIM: Probability and Statistics, Tome 15 (2011), pp. S58-S68

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It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

DOI : 10.1051/ps/2010022
Classification : 05E10, 60C05
Keywords: exchangeability, finite population statistics, Hoeffding decompositions, irreducible representations, random permutations, Specht modules, symmetric group 
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     author = {Peccati, Giovanni and Pycke, Jean-Renaud},
     title = {Hoeffding spaces and {Specht} modules},
     journal = {ESAIM: Probability and Statistics},
     pages = {S58--S68},
     publisher = {EDP-Sciences},
     volume = {15},
     year = {2011},
     doi = {10.1051/ps/2010022},
     mrnumber = {2817345},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2010022/}
}
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Peccati, Giovanni; Pycke, Jean-Renaud. Hoeffding spaces and Specht modules. ESAIM: Probability and Statistics, Tome 15 (2011), pp. S58-S68. doi: 10.1051/ps/2010022

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