In this paper, we study concave compositions, an extension of partitions that were considered by Andrews, Rhoades, and Zwegers. They presented several open problems regarding the statistical structure of concave compositions including the distribution of the perimeter and tilt, the number of summands, and the shape of the graph of a typical concave composition. We present solutions to these problems by applying Fristedt’s conditioning device on the uniform measure.

中文翻译：

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凹面组合的统计结构

在本文中，我们研究了凹组合，这是 Andrews、Rhoades 和 Zwegers 考虑的分区的扩展。他们提出了几个关于凹组合的统计结构的开放性问题，包括周长和倾斜的分布、被加数的数量以及典型凹组合的图形形状。我们通过在统一测度上应用 Fristedt 的调节装置来提出这些问题的解决方案。