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In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order ...
In mathematics, a sequence is an ... A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without ...
In mathematics, more specifically in ... The analogue of "subsequence" for nets is the notion of a "subnet". There are several different non-equivalent definitions of ...
The equivalence of the definition with the definition of compactness based on subcovers, given later in this section, is known as the Heine-Borel theorem. A more general definition that applies to all metric spaces uses the notion of a subsequence (see above). Definition.
In topology and related areas of mathematics, a subnet is a generalization of the concept of subsequence to the case of nets. The analogue of "subsequence" for nets is the notion of a "subnet". The definition is not completely straightforward, but is designed to allow as many theorems about subsequences to generalize to nets as possible.
A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring : unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences.
In mathematics, Helly's selection theorem (also called the Helly selection principle) states that a uniformly bounded sequence of monotone real functions admits a convergent subsequence. In other words, it is a sequential compactness theorem for the space of uniformly bounded monotone functions. It is named for the Austrian mathematician Eduard ...
Compute a longest common subsequence of these two strings, and let , be the random variable whose value is the length of this subsequence. Then the expected value of λ n , k {\displaystyle \lambda _{n,k}} is (up to lower-order terms) proportional to n , and the k th Chvátal–Sankoff constant γ k {\displaystyle \gamma _{k}} is the constant ...