论文标题
Raney数字上的扫描范围
Bounds on Sweep-Covers by Raney Numbers
论文作者
论文摘要
在这项工作中，我们在树木中引入了一个顶点分离器，称为扫除术，该树由祖先 - 居民与树中的所有节点的关系定义。我们证明了一类无限$δ$Δ$ - 元树在$δ$δ$Δ$ star的内部节点之间的一类无限$δ$ - 元树上，$ n $ subcovers $ p_ {δ，γ}（n）$的复发关系。然后，我们为整数组成提供了raney数字的复发关系，并表明它们为扫除覆盖物提供了较低的限制，从而使$ p_ {δ，γ}（n）=ω\ left（\ frac {\ frac {\ sqrt {\ sqrt {\ sqrt {2π} n^{Δn +δ +δ +δ + frac}} （（δ-1）n+δ+1）！（n+1）！}γ\ right）$。
In this work, we introduce a vertex separator in trees known as a sweep-cover that is defined by an ancestor-descendent relationship with all nodes in the tree. We prove the recurrence relation of sweep-covers with $n$ subcovers $P_{Δ, γ}(n)$ on a class of infinite $Δ$-ary trees with constant path lengths $γ$ between the $Δ$-star internal nodes. Then, we provide recurrence relations for Raney numbers over integer compositions and show that they provide a lower-bound for sweep-covers such that $P_{Δ, γ}(n) = Ω\left( \frac{\sqrt{2 π} n^{Δn + Δ+ \frac{3}{2}}}{e^n ((Δ-1)n+Δ+1)!(n+1)!} γ\right)$.
