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Definition & Example
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- A **binary word** is a word with letters in the alphabet $\{0,1\}$.
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- There are $2^n$ binary words of length $n$, see [A000079](https://oeis.org/A000079).
Additional information
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- 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
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Sage examples
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{{{#!sagecell
words = Words([0,1])
for word in words.iterate_by_length(3):
print word
}}}
Technical information for database usage
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- 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.