Generating functions for purely crossing partitions

The generating function for the number of purely crossing partitions of {1,...,n} is found in terms of the generating function for Bell numbers. Further results about generating functions for asymptotic moments of certain random Vandermonde matrices are derived.Comment: 10 pages; version 2 adds a citation to F. Lehner and uses the existing name "connected partitions" for what we previously called "NIS partitions.

Asymptotic *-moments of some random Vandermonde matrices

Appropriately normalized square random Vandermonde matrices based on independent random variables with uniform distribution on the unit circle are studied. It is shown that as the matrix sizes increases without bound, with respect to the expectation of the trace there is an asymptotic *-distribution, equal to that of a C[0,1]-valued R-diagonal element.Comment: 35 pages. Mathematica file available in consideration of computations of certain noncrossing cumulants. In version 1, Remark 2.1 was incorrect. This is corrected in version 2, where it is now Lemma 2.1. The proofs of Proposition 2.2 and several results in Section 4 were modified accordingly. Statements of these results remain the same, though they appear in different orde