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# 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 5 Ordered trees of size 4 [[],[],[]] [[],[[]]] [[[]],[]] [[[],[]]] [[[[]]]]
• There are $\operatorname{Cat}(n) = \frac{1}{n+1}\binom{2n}{n}$ ordered trees with $n+1$ nodes, see OEIS:A000108.

Feel free to add further combinatorial information here!

# 5. Technical information for database usage

• 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.