compile = truefalse

True means compile the iterator. The default is true.

The NearPerfectParentheses command returns an iterator that generates all n-combinations of the integers $1..2n$ that represent the positions of left parentheses in a string of n-pairs of nested parentheses. For example, the string $''()()()''$ is represented by $\left[1\,3\,5\right]$, while $''((()))''$ is represented by $\left[1\,2\,3\right]$.

Adjacent combinations differ by a single index.

$\mathrm{with}\left(\mathrm{Iterator}\right)\:$

$P≔\mathrm{NearPerfectParentheses}\left(4\right)$

$P≔\mathrm{NearPerfectParentheses}\left(4\right)$

$\mathrm{Print}\left(P\,'\mathrm{showrank}'\right)\:$

 1: 1 3 5 7
 2: 1 3 5 6
 3: 1 3 4 6
 4: 1 3 4 5
 5: 1 3 4 7
 6: 1 2 4 6
 7: 1 2 4 5
 8: 1 2 4 7
 9: 1 2 3 6
10: 1 2 3 4
11: 1 2 3 5
12: 1 2 3 7
13: 1 2 5 6
14: 1 2 5 7

$\mathrm{Number}\left(\mathrm{NearPerfectParentheses}\left(4\right)\right)$

$14$

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 4; generating all trees, sec. 7.2.1.6, generating all trees, algorithm N, near-perfect parentheses, p. 8.

The Iterator[NearPerfectParentheses] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.

The Iterator[NearPerfectParentheses] command was updated in Maple 2022.

The n parameter was updated in Maple 2022.