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subsequences

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Definitions of subsequences in various dictionaries:

noun - something that follows something else

noun - following in time

SUBSEQUENCES - In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of t...

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Subsequences description
In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence * * * * ⟨ * A * , * B * , * D * ⟩ * * * {\displaystyle \langle A,B,D\rangle } * is a subsequence of * * * * ⟨ * A * , * B * , * C * , * D * , * E * , * F * ⟩ * * * {\displaystyle \langle A,B,C,D,E,F\rangle } * obtained after removal of elements * * * * C * * * {\displaystyle C} * , * * * * E * * * {\displaystyle E} * , and * * * * F * * * {\displaystyle F} * . The relation of one sequence being the subsequence of another is a preorder. * The subsequence should not be confused with substring * * * * ⟨ * A * , * B * , * C * , * D * ⟩ * * * {\displaystyle \langle A,B,C,D\rangle } * which can be derived from the above string * * * * ⟨ * A * , * B * , * C * , * D * , * E * , * F * ⟩ * * * {\displaystyle \langle A,B,C,D,E,F\rangle } * by deleting substring * * * * ⟨ * E * , * F * ⟩ * * * {\displaystyle \langle E,F\rangle } * . The substring is a refinement of the subsequence. * The list of all subsequences for the word "apple" would be "a, ap, al, ae, app, apl, ape, ale, appl, appe, aple, apple, p, pp, pl, pe, ppl, ppe, ple, pple, l, le, e".

Subsequences description

In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence
*
*
*
* ⟨
* A
* ,
* B
* ,
* D
* ⟩
*
*
* {\displaystyle \langle A,B,D\rangle }
* is a subsequence of
*
*
*
* ⟨
* A
* ,
* B
* ,
* C
* ,
* D
* ,
* E
* ,
* F
* ⟩
*
*
* {\displaystyle \langle A,B,C,D,E,F\rangle }
* obtained after removal of elements
*
*
*
* C
*
*
* {\displaystyle C}
* ,
*
*
*
* E
*
*
* {\displaystyle E}
* , and
*
*
*
* F
*
*
* {\displaystyle F}
* . The relation of one sequence being the subsequence of another is a preorder.
* The subsequence should not be confused with substring
*
*
*
* ⟨
* A
* ,
* B
* ,
* C
* ,
* D
* ⟩
*
*
* {\displaystyle \langle A,B,C,D\rangle }
* which can be derived from the above string
*
*
*
* ⟨
* A
* ,
* B
* ,
* C
* ,
* D
* ,
* E
* ,
* F
* ⟩
*
*
* {\displaystyle \langle A,B,C,D,E,F\rangle }
* by deleting substring
*
*
*
* ⟨
* E
* ,
* F
* ⟩
*
*
* {\displaystyle \langle E,F\rangle }
* . The substring is a refinement of the subsequence.
* The list of all subsequences for the word "apple" would be "a, ap, al, ae, app, apl, ape, ale, appl, appe, aple, apple, p, pp, pl, pe, ppl, ppe, ple, pple, l, le, e".

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