一个记号

发布时间 2023-06-08 11:34:49作者: bykem

初始的 \(f\) 函数和一维 BEAF 数阵规则一样。

极限是 \(f(n,n,\cdots,n)\),记作 \(f(n,[0])\)

\(f(n,[0],\#)\) 的定义和 \(f(n,\#)\) 类似,这里 \(\#\) 只能出现数

\(f(n,[0],n,n,\cdots,n)\) 记作 \(f(n,[0],[0])\)

\(f(n,[0],[0],\#)\) 的定义和 \(f(n,[0],\#)\) 类似

一直到 \(f(n,[0],[0],\cdots,[0])\),记作 \(f(n,[0][0])\)

\(f(n,[0][0],\#)\) 的定义和 \(f(n,\#)\) 类似,这里 \(\#\) 只能出现 \([0]\) 或数

\(f(n,[0][0],[0],[0],\cdots,[0])\) 记作 \(f(n,[0][0],[0][0])\)

\(f(n,[0][0],[0][0],\#)\) 的定义和 \(f(n,[0][0],\#)\) 类似

一直到 \(f(n,[0][0],[0][0],\cdots,[0][0])\),同样记作 \(f(n,[0][0][0])\)

这样一直到 \(f(n,[0][0]\cdots[0])\),记作 \(f(n,[0]\{0\})\)

一些规则:

  • \(f(\$,\#[0])=f(\$,\#,\#,\cdots,\#)\)
  • \(f(\$,\#\{0\})=f(\$,(\#)(\#)\cdots(\#))\)
  • \(f(\$(\#\{0\}))=f(\$((\#)(\#)\cdots(\#)))\)
  • \(\#\) 为空,则替换所有 \(\#\)\(n\)(仅适用于 \([0]\)

\(f(n,[0]\{0\},[0][0]\cdots[0])=f(n,[0]\{0\},[0]\{0\})\)

\(f(n,[0]\{0\},[0]\{0\},\cdots,[0]\{0\})=f(n,[0]\{0\}[0])\)

\(f(n,[0]\{0\}[0][0]\cdots[0])=f(n,[0]\{0\}([0]\{0\}))\)

\(f(n,([0]\{0\})([0]\{0\})\cdots([0]\{0\}))=f(n,[0]\{0\}\{0\})\)

\(f(n,[0]\{0\}\{0\}\cdots\{0\})=f(n,[0](\{0\}\{0\}))\)(注意它与 \(f(n,[0]\{0\}\{0\})\) 展开顺序上的不同)

\(f(n,[0](\{0\}\{0\})[0][0]\cdots[0])=f(n,[0](\{0\}\{0\})([0]\{0\}))\)

\(f(n,[0](\{0\}\{0\})([0]\{0\})([0]\{0\})\cdots([0]\{0\}))=f(n,[0](\{0\}\{0\})([0]\{0\}\{0\}))\)

\(f(n,[0](\{0\}\{0\})([0]\{0\}\{0\}\cdots\{0\}))=f(n,[0](\{0\}\{0\})([0](\{0\}\{0\})))\)

\(f(n,([0](\{0\}\{0\}))([0](\{0\}\{0\}))\cdots([0](\{0\}\{0\})))=f(n,[0](\{0\}\{0\})\{0\})\)

\(f(n,[0](\{0\}\{0\})\{0\}\{0\}\cdots\{0\})=f(n,[0](\{0\}\{0\})(\{0\}\{0\}))\)

\(f(n,[0](\{0\}\{0\})(\{0\}\{0\})\cdots(\{0\}\{0\}))=f(n,[0](\{0\}\{0\}\{0\}))\)

\(f(n,[0](\{0\}\{0\}\cdots\{0\}))=f(n,[0]((\{0\}\{0\})))\)(注意它和 \(f(n,[0](\{0\}\{0\}))\) 展开方式上的不同)

(其实我怀疑这里已经不良定义了(悲)

那么 \(f(n,[0]((\cdots(\{0\}\{0\})\cdots)))\) 的增长率是多少?