Possible database queries for binary words: search your data / browse all statistics / browse all maps
1. Definition & Example
A binary word is a word with letters in the alphabet $\{0,1\}$.
The eight binary words of length 3 |
||||||||
000 |
001 |
010 |
011 |
100 |
101 |
110 |
111 |
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.