关于跳跃图下降的归纳
Induction on Descent in Leaper Graphs
摘要：
我们构造了一棵无限三叉树$\mathfrak{L}$，它的根是骑士，它的顶点都是斜自由跳跃者。我们定义一个斜自由跳跃的下降是它在$\mathfrak{L}$中的“地址”。我们引入了三个变换，它们将一个斜自由跳跃者的跳跃图与$\mathfrak{L}$中它的三个孩子的跳跃图联系起来。通过从骑士开始，然后应用这些变换，以推进整个$\mathfrak{L}$，我们可以建立定理的所有斜自由跳跃。我们称这种证明技术为下降归纳法，在它的帮助下，我们解决了一些关于跳跃图的问题。
英文摘要：
We construct an infinite ternary tree $\mathfrak{L}$ whose root is the knight and whose vertices are all skew free leapers. We define the descent of a skew free leaper to be its "address" within $\mathfrak{L}$. We introduce three transformations which relate the leaper graphs of a skew free leaper to the leaper graphs of its three children in $\mathfrak{L}$. By starting with the knight and then applying these transformations so as to advance throughout $\mathfrak{L}$, we can establish theorems about all skew free leapers. We call this proof technique induction on descent and with its help we resolve a number of questions about leaper graphs.
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