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Sequence where any order is equally likely
A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a
Random_permutation
Concept in combinatorics
The statistics of random permutations, such as the cycle structure of a random permutation, are of fundamental importance in the analysis of algorithms
Random_permutation_statistics
Algorithm for shuffling a finite sequence
sequence by randomly drawing an element from the list until no elements remain. The algorithm produces an unbiased permutation: every permutation is equally
Fisher–Yates_shuffle
Exact statistical hypothesis test
A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more
Permutation_test
Probability distribution on equally likely outcomes
each of its faces. Less simply, a random permutation is a permutation generated uniformly randomly from the permutations of a given set and a uniform spanning
Discrete_uniform_distribution
Cryptographic model of a random function
indistinguishable from those of a random permutation. In the ideal permutation model, an additional oracle access is given to the ideal permutation and its inverse. The
Random_oracle
Tree-based ensemble machine learning methods
random forests, in particular: Using out-of-bag error as an estimate of the generalization error. Measuring variable importance through permutation.
Random_forest
Mathematical version of an order change
In mathematics, a permutation is a bijection of a set onto itself. It can be interpreted as a new order of the members of a sequence or linear order,
Permutation
Class of functions in cryptography
pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with uniform
Pseudorandom_permutation
Family of statistical methods based on sampling of available data
are: Permutation tests (also re-randomization tests) for generating counterfactual samples Bootstrapping Cross validation Jackknife Permutation tests
Resampling_(statistics)
Sorting algorithm
deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input and checks whether
Bogosort
Divide and conquer sorting algorithm
x_{n})} is a random permutation, ( x 1 , x 2 , … , x j , x i ) {\displaystyle (x_{1},x_{2},\ldots ,x_{j},x_{i})} is also a random permutation, so the probability
Quicksort
mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation Josephus
List_of_permutation_topics
Mathematics problem
cycle of the permutation has a length of at most 50. Their survival probability is therefore equal to the probability that a random permutation of the numbers
100_prisoners_problem
Method in cryptography
a truly random permutation is the ideal FPE cipher, for large domains it is infeasible to pre-generate and remember a truly random permutation. So the
Format-preserving_encryption
Data mining technique
where the hash function used is assumed to have pseudo-random properties, the random permutation would not be used.) Now, applying hmin to both A and B
MinHash
Binary tree selected at random
application it is common to use random trees formed by inserting nodes one at a time according to a random permutation. The resulting trees are very likely
Random_binary_tree
Procedure used to randomize a deck of playing cards
the Fisher–Yates shuffle, which generates a random permutation of cards. In online gambling, the randomness of shuffling is crucial, and many sites provide
Shuffling
Independent set which is not a subset of any other independent set
C.-W.; Chen, G.-H. (1993), "Generate all maximal independent sets in permutation graphs", Internat. J. Comput. Math., 47 (1–2): 1–8, doi:10.1080/00207169308804157
Maximal_independent_set
Electoral system with lottery among ballots
solution is to extend it to random serial dictatorship (RSD), also called random priority. In this mechanism, a random permutation of the voters is selected
Random_ballot
Number generated by a random process
real Random sequence Random variable Random variate Richard Durstenfeld (July 1964). "Algorithm 235: Random permutation". Communications of the ACM. 7 (7):
Random_number
Type of cipher
the difference between the block cipher (equipped with a random key) and a random permutation. To be a bit more precise, let E be an n-bit block cipher
Block_cipher
Distribution procedure
insert fairness into this situation in the following way. Draw a random permutation of the agents from the uniform distribution. Then, let them successively
Random priority item allocation
Random_priority_item_allocation
Mathematical constant
Dickman, is a mathematical constant, which arises in the theory of random permutations and in number theory. Its value is λ = 0.62432998854355087099293638310083724
Golomb–Dickman_constant
Process of making something random
various contexts, randomization may involve: generating a random permutation of a sequence (such as when shuffling cards); selecting a random sample of a population
Randomization
Algorithmic technique using hashing
Because the symmetric group on n elements has size n!, choosing a truly random permutation from the full symmetric group is infeasible for even moderately sized
Locality-sensitive_hashing
Statistical test
significance by comparing the actual F test result to that gained from random permutations of the objects between the groups. Moreover, whilst PERMANOVA tests
Permutational analysis of variance
Permutational_analysis_of_variance
Game playing card
Leffler to create 6,000 random and unique Bingo cards. The effort is purported to have driven Leffler insane. Manual random permutation is an onerous and time-consuming
Bingo_card
Ordering obtained by a single shuffle
In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is a permutation of a set of n {\displaystyle
Riffle_shuffle_permutation
Polynomial in combinatorial mathematics
which is structured in such a way that information about how a group of permutations acts on a set can be simply read off from the coefficients and exponents
Cycle_index
Computer science problem
of independent random variables with continuous distribution F {\displaystyle F} – or alternatively the elements of a random permutation – are presented
Longest increasing subsequence
Longest_increasing_subsequence
Matrix with exactly one 1 per row and column
entries 0. An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM
Permutation_matrix
Definition and first properties of the Poisson-Dirichlet distributions
{\displaystyle j^{\operatorname {th} }} largest cycle of a uniformly distributed permutation of order N {\displaystyle N} . If for θ > 0 {\displaystyle \theta >0}
Poisson-Dirichlet distribution
Poisson-Dirichlet_distribution
mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm
Stack-sortable_permutation
Mathematical formalization of card shuffling
shuffle permutations. It forms the basis for a recommendation that a deck of cards should be riffled seven times in order to thoroughly randomize it. It
Gilbert–Shannon–Reeds_model
1991 GNU Unix command
GNU Core Utilities for creating a standard output consisting of random permutations of the input. The version of shuf bundled in GNU coreutils was written
Shuf
Type of gradient noise in computer graphics
each grid intersection. A pre-computed permutation table is used to turn a given grid coordinate into a random number. The original implementation worked
Perlin_noise
Equivalence of average-case and expected complexity
it with all permutations of the same hard distribution would be equally hard, and would produce the distribution for a random permutation. Yao's principle
Yao's_principle
Form of knot diagram
distributions on knots with a given number of petals, defined by choosing a random permutation for the branches of a petal diagram. A petal projection is a description
Petal_projection
Type of permutation of a set of elements
is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has
Derangement
Numbers parameterizing ways to partition a set
Dobiński's formula). Let the random variable X be the number of fixed points of a uniformly distributed random permutation of a finite set of size m. Then
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
the mathematical study of permutations and permutation patterns, a superpattern or universal permutation is a permutation that contains all of the patterns
Superpattern
random permutation for any secret key K {\displaystyle K} , the purpose of tweakable encryption E K T {\displaystyle E_{K}^{T}} is to mimic a random permutation
Disk_encryption_theory
Mathematical problem involving optimal stopping theory
exchangeable random permutation on { 1 , 2 , . . . , n } {\displaystyle \{1,2,...,n\}} . Now, since the only exchangeable random permutation on { 1 , 2
Secretary_problem
Algorithm for modelling sequential data
{\displaystyle PM_{\text{causal}}P^{-1}} , where P {\displaystyle P} is a random permutation matrix. An encoder consists of an embedding layer, followed by multiple
Transformer_(deep_learning)
Permutation that reverses binary numbers
In applied mathematics, a bit-reversal permutation is a permutation of a sequence of n {\displaystyle n} items, where n = 2 k {\displaystyle n=2^{k}} is
Bit-reversal_permutation
Type of sorting algorithm that works by comparing pairs of elements
either a>b or a<b, and the input is a random permutation, chosen uniformly from the set of all possible permutations of n elements, it is impossible to determine
Comparison_sort
Concept in statistics
exchangeable sequence of random variables is a finite or infinite sequence X1, X2, X3, … of random variables such that for any finite permutation σ of the indices
Exchangeable_random_variables
Apparent lack of pattern or predictability in events
In common usage, randomness is the apparent or actual lack of definite patterns or predictability in information. A random sequence of events, symbols
Randomness
Method of random selection
If the legs are drawn randomly (for reasonable definitions of "drawn randomly"), the evenness of the distribution of permutations increases with the number
Ghost_leg
Mathematical formula for the number of Young tableaux
increasing subsequences in random permutations. If σ n {\displaystyle \sigma _{n}} denotes a uniformly random permutation of order n {\displaystyle n}
Hook_length_formula
Decomposition of an integer as a sum of positive integers
determine the distribution of the longest increasing subsequence of a random permutation in terms of the Tracy–Widom distribution. Okounkov related these results
Integer_partition
Authenticated encryption mode for block ciphers
when it is used with a block cipher that is indistinguishable from a random permutation; however, security depends on choosing a unique initialization vector
Galois/Counter_Mode
Probability distribution
distribution of the length of the longest increasing subsequence of random permutations, as large-scale statistics in the Kardar-Parisi-Zhang equation, in
Tracy–Widom_distribution
U.S. conscription procedure during the Vietnam War
random permutations of the numbers 1 to 366 using random numbers selected from published tables. From the 78 permutations, 25 were selected at random
Vietnam_War_draft
meaning a permutation selected at random from the (264)! possible permutations on 64-bit blocks. Call this randomly selected permutation G. Note from
Advantage_(cryptography)
Randomized algorithm for minimum cuts
( e i ) = π ( i ) {\displaystyle w(e_{i})=\pi (i)} according to a random permutation π {\displaystyle \pi } . Removing the heaviest edge of this tree results
Karger's_algorithm
Statistical test
the matrices are subjected to random permutations many times, with the correlation being recalculated after each permutation. The significance of the observed
Mantel_test
Scheme for numbering permutations
way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion
Lehmer_code
Scheme for controlling errors in data over noisy communication channels
random interleavers (where the interleaver is a known random permutation) S-random interleaver (where the interleaver is a known random permutation with
Error_correction_code
Theory of cryptography
cryptanalysis, a random sponge function is a sponge construction where f is a random permutation or transformation, as appropriate. Random sponge functions
Sponge_function
Study of analyzing information systems in order to discover their hidden aspects
Distinguishing algorithm – the attacker can distinguish the cipher from a random permutation. Academic attacks are often against weakened versions of a cryptosystem
Cryptanalysis
US paper cryptographic system
letters A to Y in a column on the left of the page. Each row contains a random permutation of the letters A through Y. The letters in each row are grouped into
DRYAD
Extremal graph theory bound on clique-free graph edges
proof attempts to find such an independent set as follows: Consider a random permutation of the vertices of a K r + 1 {\displaystyle K_{r+1}} -free graph Select
Turán's_theorem
Large language model developed by Google AI
&\vdots &\ddots &\vdots \\0&0&0&\dots &0\end{bmatrix}}} permuted by a random permutation matrix to P M causal P − 1 {\displaystyle PM_{\text{causal}}P^{-1}}
XLNet
Divide-and-conquer algorithm for generating a random permutation of a finite set
Lumbros, Jérémie (June 2018). "MERGESHUFFLE: A Very Fast, Parallel Random Permutation Algorithm" (PDF). CEUR Workshop Proceedings. 2113: 43–52. Retrieved
Rao–Sandelius_shuffle
Digital workload distribution techniques
tasks is known in advance, it is even more efficient to calculate a random permutation in advance. This avoids communication costs for each assignment. There
Load_balancing_(computing)
American computer scientist
shown there is the construction of a strongly pseudo random permutation generator from a pseudo random function generator). Rackoff, Shafi Goldwasser, and
Charles_Rackoff
Variable representing a random phenomenon
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which
Random_variable
distribution of the number of fixed points of a uniformly distributed random permutation of { 1, ..., n }. The probability that the number of fixed points
Rencontres_numbers
Dimensionality reduction method for distributional semantics
reduced representation and random permutation." (2010): 865-870. Qasemi Zadeh, Behrang & Handschuh, Siegrfied. (2014) Random Manhattan Indexing, In Proceedings
Random_indexing
Cryptographic hash function
for the keyed permutation. Under the related-key model, the authors also presented a method that distinguishes P from a random permutation using a single
Shabal
Logical dilemma
optimal solution: one player stays put and the other player visits a random permutation of the locations. As well as being problems of theoretical interest
Rendezvous_problem
Natural number
classification of finite simple groups). In base ten, (17, 71) form the seventh permutation class of permutable primes. The sequence of residues (mod n) of a googol
17_(number)
element Random field Random function Random graph Random matrix Random measure Random multinomial logit Random naive Bayes Random permutation statistics
List_of_statistics_articles
Probability distribution
binomial distribution remains a good approximation, and is widely used. If the random variable X follows the binomial distribution with parameters n ∈ N {\displaystyle
Binomial_distribution
Algorithm for finding the shortest paths in graphs
linear order of the vertices used in Yen's second improvement by a random permutation. This change makes the worst case for Yen's improvement (in which
Bellman–Ford_algorithm
Combinatorial problem
element.[citation needed] If x {\displaystyle \mathbf {x} } is a random permutation of the integers 1 , 2 , … , n {\displaystyle 1,2,\ldots ,n} and A
Longest alternating subsequence
Longest_alternating_subsequence
Stream cipher
generated using the pseudo-random generation algorithm (PRGA). The key-scheduling algorithm is used to initialize the permutation in the array "S". "keylength"
RC4
Universal hash family used for message authentication in cryptography
distinguish AES k {\displaystyle \operatorname {AES} _{k}} from a uniform random permutation with advantage at most δ {\displaystyle \delta } . (Unless AES is
Poly1305
Count of the possible partitions of a set
a uniformly random permutation of the deck. Related to card shuffling are several other problems of counting special kinds of permutations that are also
Bell_number
Probabilistic problem-solving algorithm
between approximate randomization and permutation tests. An approximate randomization test is based on a specified subset of all permutations (which entails
Monte_Carlo_method
Sampling formula which describes the probabilities of alleles in a sample
that of the integer partition induced by a uniformly distributed random permutation. As θ → ∞, the probability that no two of the n genes are the same
Ewens's_sampling_formula
Method of shuffling a deck of cards
that are preserved by this type of shuffle, and a Gilbreath permutation is a permutation that can be formed by a Gilbreath shuffle. A Gilbreath shuffle
Gilbreath_shuffle
Block cypher operating mode
1007/3-540-57332-1_46 Craig Gentry and Zulfikar Ramzan. "Eliminating Random Permutation Oracles in the Even–Mansour Cipher" Archived 2017-08-10 at the Wayback
Xor–encrypt–xor
Collection of statistical models
closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced. Such permutation tests characterize
Analysis_of_variance
Mathematical problems related to differential equations
distribution of the length of the longest increasing subsequence of a random permutation. Together with the study of B above, it is one of the original rigorous
Riemann–Hilbert_problem
Discrete-time stochastic process
naturally lends itself to describing random permutations via their cycle structure, in addition to describing random partitions. For any positive integer
Chinese_restaurant_process
Form of scientific experiment
A randomized controlled trial (RCT) is a type of statistical experiment designed to evaluate the efficacy or safety of an intervention by minimizing bias
Randomized_controlled_trial
American statistician (1914–1991)
limit theorem: If (R1, … , Rn) is a random permutation of the numbers 1, 2, … , n that assumes every permutation with the same probability 1/n!, then
Wassily_Hoeffding
Product of numbers from 1 to n
probabilities of random permutations. In computer science, beyond appearing in the analysis of brute-force searches over permutations, factorials arise
Factorial
Block cipher
"Distinguishing TEA from a Random Permutation: Reduced Round Versions of TEA do Not Have the SAC or do Not Generate Random Numbers". Cryptography and
Tiny_Encryption_Algorithm
Game in combinatorics
in Cayley's original article) are shuffled to place them in some random permutation and are arranged in a circle with their faces up. Then, starting with
Cayley's_mousetrap
Count of permutations by cycles
kind arise in the study of permutations. In particular, the unsigned Stirling numbers of the first kind count permutations according to their number of
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Short story by Jorge Luis Borges
book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books. The narrator
The_Library_of_Babel
Discrete mathematics decomposition
two quantities coincide asymptotically on many inputs (including random permutations and pattern-avoiding point sets). Upper bounds (dynamic finger, working
Rectangulations
further constraints, this problem could easily be solved by finding a random permutation of the winners. But UEFA rules impose two additional constraints:
Random_two-sided_matching
Generalization of the one-dimensional normal distribution to higher dimensions
(univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination
Multivariate normal distribution
Multivariate_normal_distribution
Measure on group representations
problems, especially in the study of longest increasing subsequence of a random permutation σ {\displaystyle \sigma } . As a result of its importance in that
Plancherel_measure
Proven conjecture in probability theory
Diaconis, Persi; Shahshahani, Mehrdad (1981). "Generating a random permutation with random transpositions". Zeitschrift für Wahrscheinlichkeitstheorie
Aldous' spectral gap conjecture
Aldous'_spectral_gap_conjecture
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RANDOM PERMUTATION
RANDOM PERMUTATION
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Surname or Lastname
English
English : variant of Ransom.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Boy/Male
English
Son of Rand.
Surname or Lastname
English or Scottish
English or Scottish : unexplained. Possibly, as Black suggests, a reduced form of Langdon.French : from the old Germanic personal name element Lando (see Land), via the oblique case, Landonis.
Surname or Lastname
English
English : patronymic from Rand 1.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Female
English
Pet form of English Miranda, RANDY means "worthy of admiration."Â Compare with masculine Randy.Â
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English
English : variant of Brandon.
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Boy/Male
English American
Son of Rand.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
RANDOM PERMUTATION
RANDOM PERMUTATION
RANDOM PERMUTATION
RANDOM PERMUTATION
RANDOM PERMUTATION
RANDOM PERMUTATION
RANDOM PERMUTATION
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