compile = truefalse

True means compile the iterator. The default is true.

inverse = truefalse

True means return the inverse permutations. False means return the normal permutations. The default is false.

The TopologicalSorts command returns an iterator that generates the permutations of the integers 1 to n that obey specified restrictions.

The n parameter is a nonnegative integer that specifies the set of integers, 1 to n, with 0 specifying the empty set.

The rels parameter specifies the relations that restrict the permutations. The relations are true strict-inequalities between integers.

If the relation $x<y$ appears in rels, $x$ precedes $y$ in all permutations.

This iterator object has the common iterator methods.

$\mathrm{with}\left(\mathrm{Iterator}\right)\&colon;$

$T≔\mathrm{TopologicalSorts}\left(4\&comma;\left\{1<2\&comma;3<4\right\}\right)\&colon;$

$\mathrm{seq}\left(t\left[\right]\&comma;t=T\right)$

$\left[\begin{array}{cccc}1& 2& 3& 4\end{array}\right],\left[\begin{array}{cccc}1& 3& 2& 4\end{array}\right],\left[\begin{array}{cccc}1& 3& 4& 2\end{array}\right],\left[\begin{array}{cccc}3& 1& 2& 4\end{array}\right],\left[\begin{array}{cccc}3& 1& 4& 2\end{array}\right],\left[\begin{array}{cccc}3& 4& 1& 2\end{array}\right]$

$\mathrm{add}\left(1\&comma;t=T\right)$

$6$

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 2; generating all tuples and permutations, sec. 7.2.1.2, p. 63, generating all permutations, algorithm V, all topological sorts.

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

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

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

The n parameter was updated in Maple 2022.