Queries for Binary words: search statistic / browse statistics / browse maps from / browse maps to

# 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.