Communications in Number Theory and Physics

Volume 13 (2019)

Number 3

Rooted tree maps

Pages: 647 – 666



Tatsushi Tanaka (Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Kyoto-City, Japan)


Based on Hopf algebra of rooted trees introduced by Connes and Kreimer, we construct a class of linear maps on noncommutative polynomial algebra in two indeterminates, namely rooted tree maps. We also prove that their maps induce a class of relations among multiple zeta values.


Hopf algebra of rooted trees, noncommutative polynomial algebra, multiple zeta values, quasi-derivation relation, Kawashima’s relation

2010 Mathematics Subject Classification

05C05, 05C25, 11M32, 16T05

The author is grateful to scientific members and staffs in Max-Planck-Institut für Mathematik for their hospitality, where this work has been done. He is also thankful to Dr. Henrik Bachmann for helpful comments and advice. This work is also supported by Kyoto Sangyo University Research Grants.

Received 21 April 2018

Accepted 5 July 2019

Published 8 August 2022