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1992
Abstract In this chapter, we investigate some quantities based on random permutations (σ1, σ2, ... , σn) drawn from the uniform distribution over all permutations of 1, 2, ... , n. As a simple typical example of the type of random variable we study, consider the number of fixed points W in a random permutation.
A D Barbour, Lars Holst, Svante Janson
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Abstract In this chapter, we investigate some quantities based on random permutations (σ1, σ2, ... , σn) drawn from the uniform distribution over all permutations of 1, 2, ... , n. As a simple typical example of the type of random variable we study, consider the number of fixed points W in a random permutation.
A D Barbour, Lars Holst, Svante Janson
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2019
100 people leave their hats at the door at a party and pick up a completely random hat when they leave. How likely is it that at least one of them will get back their own hat? If the hats carry name tags, how difficult is it to arrange for all hats to be returned to their owner? These classical questions of probability theory can be answered relatively
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100 people leave their hats at the door at a party and pick up a completely random hat when they leave. How likely is it that at least one of them will get back their own hat? If the hats carry name tags, how difficult is it to arrange for all hats to be returned to their owner? These classical questions of probability theory can be answered relatively
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ON THE CYCLE STRUCTURE OF RANDOM PERMUTATIONS
Mathematics of the USSR-Sbornik, 1975Suppose a probability distribution is given on the set of all permutations of degree . The authors solve the problem of the joint distribution of the random variables , where is the number of cycles of length in a permutation from , in a series of cases, when the initial distribution is not uniform on all of but on certain special subsets of it. In
Tarakanov, V. E., Chistyakov, V. P.
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The generation of random permutations on the fly
Information Processing Letters, 1988How should one generate a random permutation if only a small but unpredictable subset of its domain is ever to be queried? This paper offers three different solutions to this problem. The choice between them depends on the availability of resources such as time and space.
Gilles Brassard, Sampath Kannan
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Indifferentiability of Truncated Random Permutations
2019One of natural ways of constructing a pseudorandom function from a pseudorandom permutation is to simply truncate the output of the permutation. When n is the permutation size and m is the number of truncated bits, the resulting construction is known to be indistinguishable from a random function up to \(2^{{n+m}\over 2}\) queries, which is tight.
Wonseok Choi 0002 +2 more
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The Expected order of a Random Permutation
Bulletin of the London Mathematical Society, 1991Let \(S_n\) be the symmetric group on \(n\) letters, and let \(N_n(\sigma)\) denote the group-theoretic order of \(\sigma\in S_n\). \textit{P. Erdős} and \textit{P. Turán} [Acta Math. Acad. Sci. Hung. 18, 309--320 (1967; Zbl 0235.20003)] proved that \(\log N_n(\sigma)\) has an asymptotically normal distribution with mean \(2^{-1}\log^2n\) and standard ...
Goh, William M. Y., Schmutz, Eric
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On the limitations of permuted blocked randomization
Statistics in Medicine, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Random A-permutations and Brownian motion
Proceedings of the Steklov Institute of Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Journal of the American Statistical Association, 1963
L. E. Moses, R. V. Oakford
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L. E. Moses, R. V. Oakford
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Information fractal dimension of Random Permutation Set
Chaos, Solitons and Fractals, 2023Yong Deng
exaly