On Increasing Subsequences of Random Permutations
نویسندگان
چکیده
منابع مشابه
On Increasing Subsequences of Random Permutations
Let Ln be the length of a longest increasing subsequence in a random permutation of {1, ..., n}. It is known that the expected value of Ln is asymptotically equal to 2 √ n as n gets large. This note derives upper bound on the probability that Ln − 2 √ n exceeds certain quantities. In particular, we prove that Ln − 2 √ n has order at most n1/6 with high probability. Our main result is an isoperi...
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The expected value of L n , the length of the longest increasing subsequence of a random permutation of f1; : : : ; ng, has been studied extensively. This paper presents the results of both Monte Carlo and exact computations that explore the ner structure of the distribution of L n. The results suggested that several of the conjectures that had been made about L n were incorrect, and led to new...
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We compute the limit distribution for the (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In the two–colored case our method provides a different proof of a similar result by Tracy and Widom about t...
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Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear group to obtain results about the longest increasing and decreasing subsequences in non-uniform random permutations.
متن کاملLaw of large numbers for increasing subsequences of random permutations
Let the random variable Zn,k denote the number of increasing subsequences of length k in a random permutation from Sn, the symmetric group of permutations of {1, ..., n}. We show that V ar(Zn,kn ) = o((EZn,kn ) ) as n → ∞ if and only if kn = o(n 2 5 ). In particular then, the weak law of large numbers holds for Zn,kn if kn = o(n 2 5 ); that is, lim n→∞ Zn,kn EZn,kn = 1, in probability. We also ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1996
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0095