论文标题
大规模的群集位置
Large-scale Rook Placements
论文作者
论文摘要
对于每个某些“不错”分段线性函数$ f：[0,1] \ to [0,1] $，我们考虑一个成长中的年轻图$ \ {λ（f，n）\} _ {n = 1}^{\ infty} $，通过在$ f $ of $ f $的图表下放大区域。我们计算渐近公式，以用于形状$λ（f，n）$的ROOK位置数量。我们证明，随着置换的大小的增长，均匀随机排列的归一化累积X射线表现出极限形状现象。
For each certain "nice" piecewise linear function $f:[0,1] \to [0,1]$, we consider a family of growing Young diagrams $\{λ(f,N)\}_{N=1}^{\infty}$ by enlarging the region under the graph of $f$. We compute asymptotic formulas for the number of rook placements of the shape $λ(f,N)$. We prove that the normalized cumulative X-ray of a uniformly random permutation, as the size of the permutation grows, exhibits a limit shape phenomenon.
