Duke Mathematical Journal

Algebraic aspects of increasing subsequences

Jinho Baik and Eric M. Rains

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We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial Cauchy-Littlewood sums, as well as new proofs of old formulae; relations of these expressions to orthogonal polynomials on the unit circle; and explicit bases for invariant spaces of the classical groups, together with appropriate generalizations of the straightening algorithm.

Article information

Duke Math. J. Volume 109, Number 1 (2001), 1-65.

First available in Project Euclid: 5 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]
Secondary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05E05: Symmetric functions and generalizations 60C05: Combinatorial probability


Baik, Jinho; Rains, Eric M. Algebraic aspects of increasing subsequences. Duke Math. J. 109 (2001), no. 1, 1--65. doi:10.1215/S0012-7094-01-10911-3. http://projecteuclid.org/euclid.dmj/1091737220.

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