Duke Mathematical Journal

Algebraic aspects of increasing subsequences

Jinho Baik and Eric M. Rains

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

Permanent link to this document

Digital Object Identifier

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. https://projecteuclid.org/euclid.dmj/1091737220

Export citation