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. (https://doi.org/10.1007/s00373-013-1336-6)

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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 2022 01:10
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/53179
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