Search results
Results from the WOW.Com Content Network
By contrast an increasing subsequence of a permutation is not necessarily contiguous: it is an increasing sequence obtained by omitting some of the values of the one-line notation. For example, the permutation 2453167 has the ascending runs 245, 3, and 167, while it has an increasing subsequence 2367.
In combinatorial mathematics and theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation.Any permutation may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the sequence 123...; for instance the sequence 213 represents the permutation on three elements that swaps elements 1 and 2.
Combinations and permutations in the mathematical sense are described in several articles. Described together, in-depth: Twelvefold way; Explained separately in a more accessible way: Combination; Permutation; For meanings outside of mathematics, please see both words’ disambiguation pages: Combination (disambiguation) Permutation ...
If is a substring of , it is also a subsequence, which is a more general concept. The occurrences of a given pattern in a given string can be found with a string searching algorithm . Finding the longest string which is equal to a substring of two or more strings is known as the longest common substring problem .
In mathematics, the Robinson–Schensted correspondence is a bijective correspondence between permutations and pairs of standard Young tableaux of the same shape. It has various descriptions, all of which are of algorithmic nature, it has many remarkable properties, and it has applications in combinatorics and other areas such as representation theory.
It deals with the subsequences of a randomly uniformly drawn permutation from the set {,, …,}. The theorem makes a statement about the distribution of the length of the longest increasing subsequence in the limit.
The longest common subsequence of sequences 1 and 2 is: LCS (SEQ 1,SEQ 2) = CGTTCGGCTATGCTTCTACTTATTCTA. This can be illustrated by highlighting the 27 elements of the longest common subsequence into the initial sequences: SEQ 1 = A CG G T G TCG T GCTATGCT GA T G CT G ACTTAT A T G CTA SEQ 2 = CGTTCGGCTAT C G TA C G TTCTA TT CT A T G ATT T CTA A
Arratia (1999) observes that, because the longest increasing subsequence of a random permutation has length (with high probability) approximately 2√n, it follows that a random permutation must have length at least k 2 /4 to have high probability of being a k-superpattern: permutations shorter than this will likely not contain the identity ...