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.
|Number of pages||18|
|Journal||Australasian Journal of Combinatorics|
|Publication status||Published - 2015|
- bicubic maps
- mathematical trees
- mathematical modeling