相干分布的最大展度：几何和组合的观点
Maximal Spread of Coherent Distributions: a Geometric and Combinatorial Perspective
摘要：
本文讨论了相干分布的最大展度问题。我们证明了$(X,Y)$相干分布和$α\le 2$的$\mathbb{E}|X-Y|^α$的一个精确界，并建立了相干分布与诸如二部图、共轭划分和费雷尔图等组合对象之间的新联系.我们的结果不仅对概率论家，而且对图论家，特别是对数学化学和拓扑指数研究感兴趣的人都有帮助。
英文摘要：
We discuss some open problems concerning the maximal spread of coherent distributions. We prove a sharp bound on $\mathbb{E}|X-Y|^α$ for $(X,Y)$ coherent and $α\le 2$, and establish a novel connection between coherent distributions and such combinatorial objects as bipartite graphs, conjugate partitions and Ferrer diagrams. Our results may turn out to be helpful not only for probabilists, but also for graph theorists, especially for those interested in mathematical chemistry and the study of topological indices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
