ParenthesisCodeValue on BinaryTree
The value, read in binary, of the tree's parenthesis word: each node is ( left ) right, with ( as 1 and ) as 0.
The word of a tree with n nodes has 2n digits; the empty tree's is empty, worth 0.
Called as CombinatorialStat(x, "ParenthesisCodeValue"). The head's page has its examples.
Live
Distribution
Over BinaryTrees at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000198
A decimal representation of a binary tree as a code word.
| Object | Value |
|---|---|
. | 0 |
[.,.] | 2 |
[.,[.,.]] | 10 |
[[.,.],.] | 12 |
[.,[.,[.,.]]] | 42 |
[.,[[.,.],.]] | 44 |
[[.,.],[.,.]] | 50 |
[[.,[.,.]],.] | 52 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000198 has the rest.