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The number of increasing subsequences of the random permutation

✍ Scribed by V Lifschitz; B Pittel


Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
729 KB
Volume
31
Category
Article
ISSN
0097-3165

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πŸ“œ SIMILAR VOLUMES


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Let L n be the length of a longest increasing subsequence in a random permutation of [1, ..., n]. It is known that the expected value of L n is asymptotically equal to 2 -n as n gets large. This note derives upper bound on the probability that L n &2 -n exceeds certain quantities. In particular, we

The number of permutations containing ex
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It is proved that the number of permuations on {I, 2, ... , n} with exactly one increasing subsequence of length 3 is ~(ntn3) [0,0,1,6,27,110,429, ... (Sloane A3517)]. Given a permutaion a E Sn, an abc subsequence is a set of three elements, a(i), aU), a(k), with a(i) < aU) < a(k) and i < j < k. It

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Proving a first nontrivial instance of a conjecture of Noonan and Zeilberger we Ε½ . show that the number S n of permutations of length n containing exactly r r subsequences of type 132 is a P-recursive function of n. We show that this remains true even if we impose some restrictions on the permutati

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The number of baxter permutations
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On the Law of The Iterated Logarithm for
✍ Rainer Schwabe; Allan Gut πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 490 KB

The usual law of the iterated logarithm states that the partial sums Sn of independent and identically distributed random variables can be normalized by the sequence an = d -, such that limsup,,, &/a, = t/z a. 9.. As has been pointed out by GUT (1986) the law fails if one considers the limsup along