An involution on bicubic maps and β(0, 1)-trees

Anders Claesson, Sergey Kitaev, Anna de Mier

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2 Citations (Scopus)
187 Downloads (Pure)


Bicubic maps are in bijection with β(0, 1)-trees. We introduce two new ways of decomposing β(0, 1)-trees. Using this we dene an endofunction on β(0, 1)-trees, and thus also on bicubic maps. We show that this endofunction is in fact an involution. As a consequence we are able to prove some surprising results regarding the joint equidistribution of certain pairs of statistics on trees and maps. Finally, we conjecture the number of fixed points of the involution.
Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalAustralasian Journal of Combinatorics
Issue number1
Publication statusPublished - 2015


  • bicubic maps
  • statistics
  • mathematical trees
  • mathematical modeling


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