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Recently, inspired by the Connes-Kreimer Hopf algebra of rooted trees, thesecond named author introduced rooted tree maps as a family of linear maps onthe noncommutative polynomial algebra in two letters. These give a class ofrelations among multiple zeta values, which are known to be a subclass of theso-called linear part of the Kawashima relations. In this paper we show theopposite implication, that is the linear part of the Kawashima relations isimplied by the relations coming from rooted tree maps.

Rooted tree maps and the Kawashima relations for multiple zeta values