论文标题
钩长的分布可除以两三个
Distributions of Hook Lengths Divisible by Two or Three
论文作者
论文摘要
对于固定的$ t = 2 $或$ 3 $，我们研究了$ \ {y_t（n）\} $的统计属性，这是$ n $的分区中$ t $对应的随机变量的顺序。我们表征了$ y_t（n）$的支持，并根据经验观察表明，对于大$ n $而言，支持消失了。此外，我们证明了$ y_2（n）$和$ y_3（n）$近似连续功能的质量函数的非零值。最后，我们证明，尽管质量函数无法收敛，但$ \ {y_2（n）\} $和$ \ {y_3（n）\} $的累积分布函数的累积分布功能均匀地转换为gamma分布，完成了由griffin--ono-ono-tsai启动的特征，供$ tsai for $ t \ eqe qeq 4 $。
For fixed $t = 2$ or $3$, we investigate the statistical properties of $\{Y_t(n)\}$, the sequence of random variables corresponding to the number of hook lengths divisible by $t$ among the partitions of $n$. We characterize the support of $Y_t(n)$ and show, in accordance with empirical observations, that the support is vanishingly small for large $n$. Moreover, we demonstrate that the nonzero values of the mass functions of $Y_2(n)$ and $Y_3(n)$ approximate continuous functions. Finally, we prove that although the mass functions fail to converge, the cumulative distribution functions of $\{Y_2(n)\}$ and $\{Y_3(n)\}$ converge pointwise to shifted Gamma distributions, completing a characterization initiated by Griffin--Ono--Tsai for $t \geq 4$.
