A multivariate "inv" hook formula for forests

Florent Hivert, Victor Reiner

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)33-51
Number of pages19
JournalRamanujan Journal
Issue number1-2
StatePublished - Jun 2013

Bibliographical note

Funding Information:
First author partially supported by grant ANR-06-BLAN-0380. Second author partially supported by NSF grant DMS-0601010.


  • Binary search
  • Forests
  • Free quasisymmetric functions
  • Hook formula
  • Loday-Ronco algebra
  • Moulds

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