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# Definition & Example

• A binary word is a word with letters in the alphabet $\{0,1\}$.

 the 16 Binary words of size 4 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

• There are $2^n$ binary words of length $n$, see A000079.

• Binary words of length $n$ are in natural correspondence with monotone lattice paths starting at $(0,0)$ and consisting of $n$ steps $(1,0)$ and $(0,1)$.

Feel free to add further combinatorial information here!

# Technical information for database usage

• Binary words are graded by length.
• The database contains all binary words of size at most 9.

• A binary tree is uniquely represented as a dot (empty tree) or as a sorted list of binary trees.

• Binary trees are graded by the number of internal nodes.
• The database contains all binary trees of size at most 8.

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