An involution on bicubic maps and beta(0,1)-trees
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Bicubic maps are in bijection with (0 ; 1)-trees. We introduce two new ways of decomposing (0 ; 1)-trees. Using this we de ne an endofunc- tion on (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 cer- tain pairs of statistics on trees and maps. Finally, we conjecture the number of xed points of the involution.
CitationClaesson, A.; Kitaev, S.; De Mier, A. An involution on bicubic maps and beta(0,1)-trees. "The australasian journal of combinatorics", 2015, vol. 61, núm. 1, p. 1-18.