We extend the author's formula (2011) of weighted counting of inversions on permutations to the one on alternating sign matrices. The proof is based on the sequential construction of alternating sign matrices from the unit matrix recently shown by Brualdi-Schroeder and the author (both 2017) independently.

中文翻译：

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交替符号矩阵求逆的加权计数

我们将作者的公式 (2011) 对置换的反转加权计数扩展到交替符号矩阵上的公式。该证明基于最近由 Brualdi-Schroeder 和作者（均为 2017 年）独立展示的单位矩阵的交替符号矩阵的顺序构造。