Some multivariate master polynomials for permutations,
set partitions, and perfect matchings, and their
continued fractions
Abstract.
We present Stieltjes-type and Jacobi-type continued fractions for
some "master polynomials" that enumerate permutations, set partitions
or perfect matchings with a large (some infinite) number of
simultaneous statistics. Our results contain many previously obtained
identities as special cases, providing a common refinement of all
of them. This is a joint work with Alan Sokal.