Finite multiple zeta values associated with 2-colored rooted trees

摘要

We define finite multiple zeta values (FMZVs) associated with somecombinatorial objects, which we call 2-colored rooted trees, and prove thatFMZVs associated with 2-colored rooted trees satisfying certain mildassumptions can be written explicitly as $\mathbb{Z}$-linear combinations ofthe usual FMZVs. Our result can be regarded as a generalization of Kamano'srecent work on finite Mordell-Tornheim multiple zeta values. As an application,we will give a new proof of the shuffle relation of FMZVs, which was firstproved by Kaneko and Zagier.