We present a bijection from planar reduced trees to planar rooted hypertrees, which extends Knuth's rotation correspondence between planar binary trees and planar rooted trees. The operadic counterpart of the new bijection is explained. Related to this, the space of planar reduced forests is endowed with a combinatorial Hopf algebra structure. The corresponding structure on the space of planar rooted hyperforests is also described.
Cite this article
Kurusch Ebrahimi-Fard, Dominique Manchon, On an extension of Knuth’s rotation correspondence to reduced planar trees. J. Noncommut. Geom. 8 (2014), no. 2, pp. 303–320