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The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random permutation. Quickselect will perform a partial sort on the array, as it partitions the array according to the pivot. Hence a permutation will be less disordered after quickselect has been performed. The amount of disorder that remains may be analysed with generating functions. These generating functions depend in a fundamental way on the generating functions of random permutation statistics. Hence it is of vital importance to compute these generating funct

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rdfs:label	Random permutation statistics (en)
rdfs:comment	The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random permutation. Quickselect will perform a partial sort on the array, as it partitions the array according to the pivot. Hence a permutation will be less disordered after quickselect has been performed. The amount of disorder that remains may be analysed with generating functions. These generating functions depend in a fundamental way on the generating functions of random permutation statistics. Hence it is of vital importance to compute these generating funct (en)
dcterms:subject	Combinatorics
Wikipage page ID	4915182 (xsd:integer)
Wikipage revision ID	1118739971 (xsd:integer)
Link from a Wikipage to another Wikipage	Quicksort Euler–Maclaurin summation Binomial coefficient Binomial theorem Determinant Rencontres numbers Derangement Random permutation statistics Analysis of algorithms Ordinary generating function Combinatorial species Divisor function Quickselect Combinatorics Exponential generating function Formal power series Golomb–Dickman constant Even and odd permutations Harmonic number Involution (mathematics) Telephone number (mathematics) Order (group theory) Random permutation Stirling numbers of the second kind Permutation group Stirling numbers of the first kind Falling factorial Flajolet–Sedgewick fundamental theorem Inclusion–exclusion Möbius inversion Probability generating function Putnam competition Zero is even
Link from a Wikipage to an external page	http://les-mathematiques.net http://www.math.dartmouth.edu/~pw/solutions.pdf http://les-mathematiques.u-strasbg.fr/phorum5/read.php%3F12,341672 https://math.stackexchange.com/q/259351 https://math.stackexchange.com/q/347260 https://math.stackexchange.com/q/349118 https://math.stackexchange.com/q/495487 https://math.stackexchange.com/q/73896
sameAs	Random permutation statistics Random permutation statistics Random permutation statistics
dbp:wikiPageUsesTemplate	dbt:Cite_document dbt:In_lang dbt:Main dbt:OEIS dbt:Original_research dbt:Reflist dbt:OEIS2C
has abstract	The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random permutation. Quickselect will perform a partial sort on the array, as it partitions the array according to the pivot. Hence a permutation will be less disordered after quickselect has been performed. The amount of disorder that remains may be analysed with generating functions. These generating functions depend in a fundamental way on the generating functions of random permutation statistics. Hence it is of vital importance to compute these generating functions. The article on random permutations contains an introduction to random permutations. (en)
prov:wasDerivedFrom	wikipedia-en:Random_permutation_statistics?oldid=1118739971&ns=0
page length (characters) of wiki page	51526 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Random_permutation_statistics
is Link from a Wikipage to another Wikipage of	Cycle index Derangement List of permutation topics Random permutation statistics 100 prisoners problem Affine symmetric group Golomb–Dickman constant Symbolic method (combinatorics) Inclusion–exclusion principle Michelle L. Wachs List of statistics articles Random permutation Stirling numbers and exponential generating functions in symbolic combinatorics Random Permutation Statistics Random permutation statistic Stirling numbers of the second kind Stirling numbers of the first kind Permutation statistic Permutation statistics
is Wikipage redirect of	Random Permutation Statistics Random permutation statistic Permutation statistic Permutation statistics
is foaf:primaryTopic of	wikipedia-en:Random_permutation_statistics

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