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

Anders Claesson, Sergey Kitaev, Anna de Mier

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.
LanguageEnglish
Pages1-18
Number of pages18
JournalAustralasian Journal of Combinatorics
Volume61
Issue number1
Publication statusPublished - 2015

Fingerprint

Involution
Equidistribution
Bijection
Fixed point
Statistics

Keywords

  • bicubic maps
  • statistics
  • mathematical trees
  • mathematical modeling

Cite this

Claesson, Anders ; Kitaev, Sergey ; de Mier, Anna. / An involution on bicubic maps and β(0, 1)-trees. In: Australasian Journal of Combinatorics. 2015 ; Vol. 61, No. 1. pp. 1-18.
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An involution on bicubic maps and β(0, 1)-trees. / Claesson, Anders; Kitaev, Sergey; de Mier, Anna.

In: Australasian Journal of Combinatorics, Vol. 61, No. 1, 2015, p. 1-18.

Research output: Contribution to journalArticle

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