Abstract
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.
Citation
Jinho Baik. Eric M. Rains. "Algebraic aspects of increasing subsequences." Duke Math. J. 109 (1) 1 - 65, 15 July 2001. https://doi.org/10.1215/S0012-7094-01-10911-3
Information