Generating functions for purely crossing partitions
Kenneth J. Dykema
TL;DR
This paper derives the generating function for purely crossing partitions and applies it to analyze asymptotic moments of specific random Vandermonde matrices.
Contribution
It introduces a new generating function for purely crossing partitions and connects it to the moments of random Vandermonde matrices.
Findings
Generated explicit formulas for purely crossing partitions.
Linked partition generating functions to moments of Vandermonde matrices.
Provided new tools for analyzing asymptotic behaviors in random matrix theory.
Abstract
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.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Combinatorial Mathematics · Bayesian Methods and Mixture Models