Duke Mathematical Journal
- Duke Math. J.
- Volume 109, Number 1 (2001), 1-65.
Algebraic aspects of increasing subsequences
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.
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