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It is well known that sometimes Euler sums (i.e., alternating multiple zeta
values) can be expressed as $\Q$-linear combinations of multiple zeta values
(MZVs). In her thesis Glanois presented a criterion for a motivic Euler sums
(MES) to be unramified, namely, expressible as $\Q$-linear combinations of
motivic MZVs. By applying this criterion we present a few families of such
unramified MES in two groups. In one such group we can further prove the
concrete identities relating the MES to the motivic MZVs, determined up to
rational multiple of a motivic Riemann zeta value by a result of Brown.
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