# Difference between revisions of "Bird's array notation"

Bird's array notation is a parallel notation to BEAF.

## Linear arrays

• Rule 1. With one or two entries, we have $$\{a\} = a$$, $$\{a,b\} = a^b$$.
• Rule 2. If the last entry is 1, it can be removed: $$\{\#,1\} = \{\#\}$$.
• Rule 3. If the second entry is 1, the value is just the first entry: $$\{a,1 \#\} = a$$.
• Rule 4. If the third entry is 1:
$$\{a,b,1,1,\cdots,1,1,c \#\} = \{a,a,a,a,\cdots,a,\{a,b-1,1,1,\cdots,1,1,c \#\},c-1 \#\}$$
• Rule 5. Otherwise:
$$\{a,b,c \#\} = \{a,\{a,b-1,c \#\},c-1 \#\}$$

### Example

\begin{eqnarray*} \{3,3,1,2\} &=& \{3,3,\{3,2,1,2\},1\} \\ &=& \{3,3,\{3,3,\{3,1,1,2\},1\}\} \\ &=& \{3,3,\{3,3,3\}\} \\ &=& \{3,3,\{3,\{3,2,3\},2\}\} \\ &=& \{3,3,\{3,\{3,\{3,1,3\},2\},2\}\} \\ &=& \{3,3,\{3,\{3,3,2\},2\}\} \\ &=& \{3,3,\{3,\{3,\{3,2,2\},1\},2\}\} \\ &=& \{3,3,\{3,\{3,\{3,\{3,1,2\},1\}\},2\}\} \\ &=& \{3,3,\{3,\{3,\{3,3\}\},2\}\} \\ &=& \{3,3,\{3,7625597484987,2\}\} \\ &=& 3\uparrow^{3\uparrow\uparrow7625597484987}3