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Annals of Combinatorics

, Volume 16, Issue 4, pp 847–870 | Cite as

Limiting Distributions for the Number of Inversions in Labelled Tree Families

  • Alois PanholzerEmail author
  • Georg Seitz
Article

Abstract

We consider the so-called simple families of labelled trees, which contain, e.g., ordered, unordered, binary, and cyclic labelled trees as special instances, and study the global and local behaviour of the number of inversions. In particular, we obtain limiting distribution results for the total number of inversions as well as the number of inversions induced by the node labelled j in a random tree of size n.

Mathematics Subject Classification

05C05 60F05 05A16 

Keywords

inversions simply generated trees limiting distributions 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienWienAustria

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