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In mathematics, a subsequence of some sequence is a new sequence which is formed from the original sequence by deleting some of the elements without disturbing the relative positions of the remaining elements. ## Example

As an example,
## Applications

Subsequences have applications to computer science, especially in the discipline of Bioinformatics, where computers are used to compare, analyze, and store DNA strands.## Substring vs. subsequence

In computer science, string is often used as a synonym for sequence, but it is important to note that substring and subsequence are not synonyms. Substrings are consecutive parts of a string, while subsequences need not be. This means that a substring of a string is always a subsequence of the string, but the subsequence of a string is not always a substring of the string.
## See also

## References

Formally, suppose that X is a set and that (a_{k})_{k ∈ K} is a sequence in X, where K = {1,2,3,...,n} if (a_{k}) is a finite sequence and K = N if (a_{k}) is an infinite sequence. Then, a subsequence of (a_{k}) is a sequence of the form $(a\_\{n\_r\})$ where (n_{r}) is a strictly increasing sequence in the index set K.

- $<\; B,C,D,G\; >$

- $<\; A,C,B,D,E,G,C,E,D,B,G\; >$,

Given two sequences X and Y, a sequence G is said to be a common subsequence of X and Y, if G is a subsequence of both X and Y. For example, if

- $X\; =\; <\; A,C,B,D,E,G,C,E,D,B,G\; >$ and

- $Y\; =\; <\; B,E,G,C,F,E,U,B,K\; >$

- $G\; =\; <\; B,E,E\; >$

This would not be the longest common subsequence, since G only has length 3, and the common subsequence < B,E,E,B > has length 4. The longest common subsequence of X and Y is < B,E,G,C,E,B >.

Take two strands of DNA, say :

ORG_{1} = `ACGGTGTCGTGCTATGCTGATGCTGACTTATATGCTA`

ORG_{2} = `CGTTCGGCTATCGTACGTTCTATTCTATGATTTCTAA`

Subsequences are used to determine how similar the two strands of DNA are, using the DNA bases: adenine, guanine, cytosine and thymine.

- subsequential limit
- limit superior and limit inferior
- longest common subsequence problem
- longest increasing subsequence problem
- Erdős–Szekeres theorem

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Last updated on Thursday September 25, 2008 at 11:02:08 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Thursday September 25, 2008 at 11:02:08 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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