An involution on bicubic maps and \beta(0,1)-trees
Combinatorics
2013-06-25 v2
Abstract
Bicubic maps are in bijection with \beta(0,1)-trees. We introduce two new ways of decomposing \beta(0,1)-trees. Using this we define an endofunction on \beta(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.
Cite
@article{arxiv.1210.3219,
title = {An involution on bicubic maps and \beta(0,1)-trees},
author = {Anders Claesson and Sergey Kitaev and Anna de Mier},
journal= {arXiv preprint arXiv:1210.3219},
year = {2013}
}