A multivariate "inv" hook formula for forests

A previous talk in this seminar (Feb. 12, 2010) discussed D.E. Knuth's hook-formula (1973) counting linear extensions of forests, as well as Bjoerner and Wachs q-hook-formula (1989) enumerating these linear extensions according to their major index statistic. Bjoerner and Wachs also showed that this same q-hook formula enumerates the linear extensions for certain kinds of forests according to their inversion number ("inv") statistic.

This talk will explain will a multivariate generalization of this "inv" q-hook-formula, closely related to joint work with D. Stanton on invariant theory of the general linear group over a finite field F_q.