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In this paper, we prove that a partial tilting $A^{(m)}$-module $T$ is a tilting $A^{(m)}$-module if and only if $\\delta (T)=\\delta (A^{(m)})$, and that every partial tilting $A^{(m)}$-module has complements. As an application, we deduce that the tilting quiver $\\mathscr{K}_{A^{(m)}}$ of $A^{(m)}$ is connected. 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