论文标题
随机整数组成中的协方差
Covariance within Random Integer Compositions
论文作者
论文摘要
修复一个正整数$ n $。选择一个$ 2^{n-1} $的可能性均匀的$ n $的添加成分$ξ$。 $ξ$中的零件数量与$ξ$中的最大零件之间的相互作用是我们的重点。这些数量之间的相关性$ρ（n）$是负数也就不足为奇了。我们早些时候提供了尚无定论的证据，表明$ \ lim_ {n \ to \ infty}ρ（n）$严格小于零。这一结果的证明将暗示渐近依赖性。现在，我们在这样的不可预见的结果中撤回了推定。当$ξ$是1份的构图时，也适用类似的实验发现，即仅拥有零件$ \ geq 2 $。
Fix a positive integer $N$. Select an additive composition $ξ$ of $N$ uniformly out of $2^{N-1}$ possibilities. The interplay between the number of parts in $ξ$ and the maximum part in $ξ$ is our focus. It is not surprising that correlations $ρ(N)$ between these quantities are negative; we earlier gave inconclusive evidence that $\lim_{N \to \infty} ρ(N)$ is strictly less than zero. A proof of this result would imply asymptotic dependence. We now retract our presumption in such an unforeseen outcome. Similar experimental findings apply when $ξ$ is a 1-free composition, i.e., possessing only parts $\geq 2$.
