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COMBINATORICS
1998

Increasing Subsequences and the Classical Groups

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Increasing Subsequences and the Classical Groups
We show that the moments of the trace of a random unitary matrix have combinatorial interpretations in terms of longest increasing subsequences of permutations. To be precise, we show that the 2n-th moment of the trace of a random k-dimensional unitary matrix is equal to the number of permutations of length n with no increasing subsequence of length greater than k. We then generalize this to other expectations over the unitary group, as well as expectations over the orthogonal and symplectic groups. In each case, the expectations count objects with restricted “increasing subsequence” length.
Eric M. Rains
Added 21 Dec 2010
Updated 21 Dec 2010
Type Journal
Year 1998
Where COMBINATORICS
Authors Eric M. Rains
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