Hydrodynamical methods for analyzing longest increasing subsequences

Authors:
Piet Groeneboom
Affiliations:
Delft University of Technology, Faculty of ITS, Mekelweg 4, 2628 CD Delft, Netherlands and Free University, Faculty of Exact Sciences, de Boelelaan 1081a, 1081 HV Amsterdam, Netherlands
Venue:
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Year:
2002

Citing 1
Cited 1

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Combinatorics, Probability and Computing

Longest increasing subsequences in sliding windows

Theoretical Computer Science

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Abstract

Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1 .... , n, for the uniform distribution on the set of permutations. We discuss the "hydrodynamical approach" to the analysis of the limit behavior, which probably started with Hammersley (Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1 (1972) 345-394) and was subsequently further developed by several authors. We also give two proofs of an exact (non-asymptotic) result, announced in Rains (preprint, 2000).