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

Kitaev, Sergey and de Mier, Anna (2014) Enumeration of fixed points of an involution on β(1, 0)-trees. Graphs and Combinatorics, 30 (5). pp. 1207-1221.

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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.

    ORCID iDs

    Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647 and de Mier, Anna;
    • Item type:Article
      ID code:53179
      Dates:
      Date
      Event
      1 September 2014
      Published
      2 July 2013
      Published Online
      18 May 2013
      Accepted
      Notes:The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-013-1336-6
      Keywords:planar maps, description trees, fixed points, enumeration, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Theoretical Computer Science
      Subjects:Science > Mathematics > Electronic computers. Computer science
      Department:Faculty of Science > Computer and Information Sciences
      Depositing user: Pure Administrator
      Date deposited:02 Jun 2015 09:46
      Last modified:23 Sep 2021 04:42
      Related URLs:
      URI:https://strathprints.strath.ac.uk/id/eprint/53179
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