Multivariate Fuss-Narayana polynomials and their application to random   matrices
  It has been shown recently that the limit moments of $W(n)=B(n)B^{*}(n)$, where B(n) is a product of $p$ independent rectangular random matrices, are certain homogenous polynomials in the asymptotic dimensions of these matrices. Using the combinatorics of noncrossing partitions, we explicitly determine these polynomials and show that they are closely related to polynomials which can be viewed as multivariate Fuss-Narayana polynomials. Using this result, we compute the moments of the n-fold free multiplicative convolution of Marchenko-Pastur distributions with arbitrary shape parameters. 
Romuald Lenczewski and Rafal Salapata
math.CO math.PR