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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.

Additional information

• 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!

References

Sage examples

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.