CUE联合矩问题的一种组合方法
A Combinatorial Approach to the CUE Joint Moment Problem
AI总结：
本文通过组合方法给出了CUE联合矩的精确表达式，统一了相关文献结果，并证明了Basor等人的猜想。
AI中文摘要：
本文中，我们给出了单位圆上所有CUE联合矩的精确组合表达式，适用于所有指数均为正偶数的情况，并由此得到了相应的渐近行为。我们提供了这些量的两种等价表达式：第一种是涉及Kostka数的求和；第二种与整数矩阵（幻方）的计数相关。作为我们结果的一个应用，我们统一了文献中许多此前互不关联的结果。此外，我们证明了Basor等人（2018）关于不规则共形块结构的一个猜想。
英文摘要：
In this paper, we give exact combinatorial expressions for all CUE joint moments on the unit circle, in the case that all exponents are even positive integers, yielding the corresponding asymptotics. We offer two equivalent expressions for these quantities: the first is a sum involving Kostka numbers; the second is related to counting integer matrices (magic squares). As an application of our results, we unify many results in the literature, which were previously disconnected. Moreover, we prove a conjecture of Basor et al. (2018) regarding an irregular conformal block structure.
