A direct saddle-point analysis (without relying on any modular forms or functional equations) is developed to establish the asymptotics of Fishburn matrices and a large number of other variants with a similar sum-of-finite-product form for their (formal) generating functions. In addition to solving some conjectures, the application of our saddle-point approach to the distributional aspects of statistics on Fishburn matrices is also examined with many new limit theorems characterized, representing the first of their kind for such structures.

中文翻译：

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Fishburn矩阵的渐近统计和归纳

直接鞍点分析（不依赖任何模块化形式或函数方程式）被开发出来，以建立Fishburn矩阵和许多其他变式的渐近性，它们的（形式）生成具有相似的有限积和形式。功能。除了解决一些猜想之外，我们还利用许多新的极限定理研究了鞍点法在菲什伯恩矩阵统计分布方面的应用，这是此类结构的第一个极限定理。