The ordinary and symmetrized partition rank and crank moments of higher order have been extensively studied. If we assign a weight \(\sharp (\lambda )\) for the rank case and a weight \(\omega (\lambda )\) for the crank case, where \(\sharp (\lambda )\) and \(\omega (\lambda )\), respectively, denote the number of parts in the partition \(\lambda \) and the number of ones in \(\lambda \), it will be shown that such weighted ordinary and symmetrized rank and crank moments of higher order are closely related to the corresponding rank and crank moments when the order is odd.

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加权分区等级和曲柄力矩II。奇数阶矩

对普通和对称的高阶分隔等级和曲柄力矩进行了广泛的研究。如果我们为权重案例分配权重\（\ sharp（\ lambda）\），为曲柄案例分配权重\（\ omega（\ lambda）\），其中\（\ sharp（\ lambda）\）和\ （\ omega（\ lambda）\）分别表示分区\（\ lambda \）中的部分数和\（\ lambda \）中的部分数，这将表明这种加权的普通级和对称级当阶数奇数时，高阶曲柄力矩和曲柄力矩与相应的阶跃和曲柄力矩紧密相关。