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

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.

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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

Published: 15 July 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1007.05096
MathSciNet: MR1844203
Digital Object Identifier: 10.1215/S0012-7094-01-10911-3

Subjects:
Primary: 05E15
Secondary: 05A15, 05E05, 60C05

Rights: Copyright © 2001 Duke University Press

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Vol.109 • No. 1 • 15 July 2001
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