Enumeration of fixed points of an involution on β(1, 0)-trees

Sergey Kitaev, Anna de Mier

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Abstract

β(1, 0)-trees provide a convenient description of rooted non-separable planar maps. The involution h on β(1, 0)-trees was introduced to prove a complicated equidistribution result on a class of pattern-avoiding permutations. In this paper, we describe and enumerate fixed points of the involution h. Intriguingly, the fixed points are equinumerous with the fixed points under taking the dual map on rooted non-separable planar maps, even though the fixed points do not go to each other under the know (natural) bijection between the trees and the maps.
Original languageEnglish
Pages (from-to)1207-1221
Number of pages15
JournalGraphs and Combinatorics
Volume30
Issue number5
Early online date2 Jul 2013
DOIs
Publication statusPublished - 1 Sep 2014

Keywords

  • planar maps
  • description trees
  • fixed points
  • enumeration

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