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Algebraic aspects of increasing subsequences

Baik, Jinho and Rains, Eric M. (2001) Algebraic aspects of increasing subsequences. Duke Mathematical Journal, 109 (1). pp. 1-65. ISSN 0012-7094. doi:10.1215/S0012-7094-01-10911-3.

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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.

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Additional Information:© 2001 Duke University Press. Received 23 February 2000. Revision received 26 September 2000. Baik’s work supported in part by a Sloan Doctoral Foundation Fellowship. We would like to acknowledge the following people for helpful discussions: Kurt Johansson for telling us about the processes generalized in Section 7, Richard Stanley for telling us about the references for that section, Peter Shor for spotting flaws in earlier versions of the algorithms of Section 8, and Christian Krattenthaler for helpful comments on Section 5. We would also like to thank Jeff Lagarias, Andrew Odlyzko, and Neil Sloane for helpful comments and enthusiasm.
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Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:1
Classification Code:2000 Mathematics Subject Classification. Primary 05E15
Record Number:CaltechAUTHORS:20171004-073359453
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Official Citation: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.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82025
Deposited By: Tony Diaz
Deposited On:04 Oct 2017 17:17
Last Modified:15 Nov 2021 19:47

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