Bilabelled increasing trees and hook-length formulae

  • Authors:

  • Markus Kuba;Alois Panholzer

  • Affiliations:

  • Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/104, 1040 Wien-HTL Wien 5 Spengergasse, Spengergasse 20, 1050 Wien, Austria;Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2012

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Abstract

We introduce two different kinds of increasing bilabellings of trees, for which we provide enumeration formulae. One of the bilabelled tree families considered is enumerated by the reduced tangent numbers and is in bijection with a tree family introduced by Poupard [11]. Both increasing bilabellings naturally lead to hook-length formulae for trees and forests; in particular, one construction gives a combinatorial interpretation of a formula for labelled unordered forests obtained recently by Chen et al. [1].