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{\bf Alexei Borodin}
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{\bf Longest Increasing Subsequences of Random Colored Permutations}
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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 the longest increasing subsequences
of signed permutations (math.CO/9811154).

Our main idea is to reduce the `colored' problem to the case
of usual random permutations using certain combinatorial results
and elementary probabilistic arguments.



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