A multivariate "maj" hook formula for forests

A "forest" here means a partially ordered set in which each element is covered by at most one other element. In his 1973 "Art of Computer Programming", D.E. Knuth noted a simple product formula counting linear extensions of a forest. Bjoerner and Wachs generalized this in 1989 to a formula that enumerates the linear extensions according to their major index statistic.

This talk will review Stanley's theory of P-partitions and deduce from it a very simple multivariate generalization of this major index q-hook-formula. This generalization has another interesting specialization to a recent formula of Chapoton, Hivert, Novelli and Thibon.