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We establish an identity amongst certain differential operators applied to aformal power-series. As a corollary we obtain an explicit depth reductionresult for alternating MZV's of the form $\zeta(1,\ldots,1,\overline{2m})$,which resolves a conjecture posed earlier by the third author.

Differential operators and a depth reduction for the alternating multiple zeta values $\zeta(1, \ldots, 1, \overline{2m})$