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Constructions of Beyond-Birthday Secure PRFs from Random Permutations, Revisited [PDF]
Entropy, 2021 In CRYPTO 2019, Chen et al. showed how to construct pseudorandom functions (PRFs) from random permutations (RPs), and they gave one beyond-birthday secure construction from sum of Even-Mansour, namely SoEM22 in the single-key setting.
Jiehui Nan, Ping Zhang, Honggang Hu
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Exact testing with random permutations. [PDF]
Test (Madr), 2018 When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods based on random permutations tend to be seen as approximate.
Hemerik J, Goeman J.
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Cycles in Mallows random permutations
Random Structures and Algorithms, 2023 AbstractWe study cycle counts in permutations of drawn at random according to the Mallows distribution. Under this distribution, each permutation is selected with probability proportional to , where is a parameter and denotes the number of inversions of .
Jimmy He +2 more
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Spherically symmetric random permutations
Random Structures and Algorithms, 2019 We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group Sn and are consistent as n varies. The extreme infinitely spherically symmetric permutation‐valued processes are identified for the Hamming, Kendall‐tau and Cayley metrics. The proofs in all three cases are based on a unified approach through
Vadim Gorin
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Random permutations and queues
Advances in Applied Mathematics, 2023 28 ...
Alexander V. Gnedin, Dudley Stark
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Pattern Avoidance for Random Permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences and a ...
Harry Crane, Stephen DeSalvo
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Permutations on the Random Permutation [PDF]
The Electronic Journal of Combinatorics, 2015 The random permutation is the Fraïssé limit of the class of finite structures with two linear orders. Answering a problem stated by Peter Cameron in 2002, we use a recent Ramsey-theoretic technique to show that there exist precisely 39 closed supergroups of the automorphism group of the random permutation, and thereby expose all symmetries of this ...
Julie Linman, Michael Pinsker
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Random permutations and their discrepancy process [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 Let $\sigma$ be a random permutation chosen uniformly over the symmetric group $\mathfrak{S}_n$. We study a new "process-valued" statistic of $\sigma$, which appears in the domain of computational biology to construct tests of similarity between ordered ...
Guillaume Chapuy
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Enumeration of Permutation Classes and Weighted Labelled Independent Sets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cells filled with permutations. We consider many cases, where restricted to a permutation class, the staircase encoding becomes a bijection ...
Christian Bean +2 more
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The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 We obtain an explicit formula for the variance of the number of $k$-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest $k$-alternating subsequence in random permutations ...
Altar Çiçeksiz +2 more
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