Lattice paths and branched continued fractions. II. Multivariate Lah polynomials and Lah symmetric functions

Mathias Pétréolle, Alan D. Sokal

We introduce the generic Lah polynomials $L_{n,k}(\varphi )$, which enumerate unordered forests of increasing ordered trees with a weight ${\varphi }_i$ for each vertex with $i$ children. We show…