On longest increasing subsequences in random permutations
نویسندگان
چکیده
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 conjectures, some of which have been proved recently by Jinho Baik, Percy Deift, and Kurt Johansson. In particular, the standard deviation of L n is of order n 1=6 , contrary to earlier conjectures. This paper also explains some regular patterns in the distribution of L n .
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