Björner and Wachs provided two q-generalizations of Knuth's hook formula counting linear extensions of forests: one involving the major index statistic, and one involving the inversion number statistic. We prove a multivariate generalization of their inversion number result, motivated by specializations related to the modular invariant theory of finite general linear groups.
Bibliographical noteFunding Information:
First author partially supported by grant ANR-06-BLAN-0380. Second author partially supported by NSF grant DMS-0601010.
- Binary search
- Free quasisymmetric functions
- Hook formula
- Loday-Ronco algebra