On an extension of Knuth's rotation correspondence to reduced planar trees

TL;DR

This paper extends Knuth's rotation correspondence to reduced planar trees, establishing a bijection with planar rooted hypertrees and exploring associated operadic and Hopf algebra structures.

Contribution

It introduces a novel bijection between planar reduced trees and hypertrees, extending classical combinatorial correspondences and analyzing their algebraic structures.

Findings

Established a bijection between planar reduced trees and hypertrees

Defined a Hopf algebra structure on the space of planar reduced forests

Connected the combinatorial structures to operadic frameworks

Abstract

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.