Journal of Noncommutative Geometry


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Volume 8, Issue 2, 2014, pp. 303–320
DOI: 10.4171/JNCG/157

Published online: 2014-07-18

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

Kurusch Ebrahimi-Fard[1] and Dominique Manchon[2]

(1) Universidad Autónoma de Madrid, Spain
(2) Université Blaise Pascal, Aubière, France

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.

Keywords: Trees, hypertrees, rotation correspondence, operads, Hopf algebras

Ebrahimi-Fard Kurusch, Manchon Dominique: On an extension of Knuth’s rotation correspondence to reduced planar trees. J. Noncommut. Geom. 8 (2014), 303-320. doi: 10.4171/JNCG/157