Hoeffding spaces and Specht modules

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.Comment: 13 page

New Karhunen-Loeve expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs

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