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A multivariate “inv” hook formula for forests

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Abstract

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.

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Authors and Affiliations

  1. Laboratoire de Recherche en Informatique (UMR CNRS 8623), Bâtiment 650, Univ. Paris Sud 11, 91405, Orsay Cedex, France

    Florent Hivert

  2. LITIS, Université de Rouen, Avenue de l’Universit’e, 76801, Saint Étienne du Rouvray, France

    Florent Hivert

  3. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Victor Reiner

Authors
  1. Florent Hivert
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  2. Victor Reiner
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Correspondence to Victor Reiner.

Additional information

To Mourad Ismail and Dennis Stanton

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

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Hivert, F., Reiner, V. A multivariate “inv” hook formula for forests. Ramanujan J 31, 33–51 (2013). https://doi.org/10.1007/s11139-012-9390-x

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  • DOI: https://doi.org/10.1007/s11139-012-9390-x

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