RootedForests

The forests of rooted labeled trees on $\{1, \dots, n\}$, each element a length-$n$ parent array (entry $0$ marks a root). Count $(n+1)^{n-1}$.

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RootedForests(n)the rooted forests on $\{1, \dots, n\}$, as parent arrays

Typed signatures

Type	Package	Applies
(integer<0..>) -> indexed_collection<rooted_forest>	combinatorics	always

Domain: Collections

Examples

Basic #

$(3+1)^{2} = 16$

live ↗

In$\mathrm{Count}(\mathrm{RootedForests}(3))$Out$16$

Parent arrays; $0$ marks a root

live ↗

In$\mathrm{Take}(\mathrm{RootedForests}(2), 3)$Out$\bigl\lbrack{\operatorname{RootedForest}}([0, 1]), {\operatorname{RootedForest}}([2, 0]), {\operatorname{RootedForest}}([0, 0])\bigr\rbrack$

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Examples	2
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