This paper is the second in a series of planned papers which provide first bijective proofs of alternating sign matrix results. Based on the main result from the first paper, we construct a bijective proof of the enumeration formula for alternating sign matrices and of the fact that alternating sign matrices are equinumerous with descending plane partitions. We are also able to refine these bijections by including the position of the unique $1$ in the top row of the matrix. Our constructions rely on signed sets and related notions. The starting point for these constructions were known ``computational'' proofs, but the combinatorial point of view led to several drastic modifications. We also provide computer code where all of our constructions have been implemented.

中文翻译：

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ASM 定理的双射证明第二部分：ASM 枚举和 ASM-DPP 关系

这篇论文是一系列计划论文中的第二篇，它提供了交替符号矩阵结果的第一个双射证明。基于第一篇论文的主要结果，我们构造了交替符号矩阵枚举公式的双射证明，以及交替符号矩阵与下降平面分区相等的事实。我们还可以通过在矩阵的顶行中包含唯一的 $1$ 的位置来优化这些双射。我们的构造依赖于有符号集和相关概念。这些构造的起点是已知的“计算”证明，但组合的观点导致了一些剧烈的修改。我们还提供计算机代码，其中我们的所有结构都已实现。