@unpublished{20572,
  abstract     = {We present an elementary non-recursive formula for the multivariate moments
of the Dirichlet distribution on the standard simplex, in terms of the pattern
inventory of the moments' exponents. We obtain analog formulas for the
multivariate moments of the Dirichlet-Ferguson and Gamma measures. We further
introduce a polychromatic analogue of Ewens sampling formula on colored integer
partitions, discuss its relation with suitable extensions of Hoppe's urn model
and of the Chinese restaurant process, and prove that it satisfies an adapted
notion of consistency in the sense of Kingman.},
  author       = {Dello Schiavo, Lorenzo and Quattrocchi, Filippo},
  booktitle    = {arXiv},
  keywords     = {Dirichlet distribution, Ewens sampling formula, Hoppe urn model, colored partitions},
  title        = {{Multivariate Dirichlet moments and a polychromatic Ewens sampling formula}},
  doi          = {10.48550/arXiv.2309.11292},
  year         = {2023},
}