Possible database queries for ordered trees: search your data / browse all statistics / browse all maps
1. Definition & Example
An ordered tree is a rooted tree where the children of each node are ordered.
Equivalently, an ordered tree is recursively defined to be either a leaf (external node) or an ordered list of ordered trees (internal node).
The five ordered trees with 4 nodes |
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There are $\operatorname{Cat}(n) = \frac{1}{n+1}\binom{2n}{n}$ ordered trees with $n+1$ nodes, see OEIS:A000108.
2. FindStat representation and coverage
An ordered tree is uniquely represented as an empty list (leaf) or as a sorted list of ordered trees (internal node).
Ordered trees are graded by its number of nodes.
- The database contains all ordered trees of size at most 9.
3. Additional information
Feel free to add further combinatorial information here!
4. References
5. Sage examples