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1. 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.
2. 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!
3. References
4. Sage examples
5. 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.