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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Recent progress in algebraic combinatorics

Author: Richard P. Stanley
Journal: Bull. Amer. Math. Soc. 40 (2003), 55-68
MSC (2000): Primary 05E99; Secondary 05E05, 14C05, 15A18, 60C05
Published electronically: October 11, 2002
MathSciNet review: 1943133
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Abstract: We survey three recent breakthroughs in algebraic combinatorics. The first is the proof by Knutson and Tao, and later Derksen and Weyman, of the saturation conjecture for Littlewood-Richardson coefficients. The second is the proof of the $n!$ and $(n+1)^{n-1}$ conjectures by Haiman. The final breakthrough is the determination by Baik, Deift, and Johansson of the limiting behavior of the length of the longest increasing subsequence of a random permutation.

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Additional Information

Richard P. Stanley
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Received by editor(s): October 23, 2000
Received by editor(s) in revised form: January 4, 2002
Published electronically: October 11, 2002
Additional Notes: Partially supported by NSF grant #DMS-9988459
Article copyright: © Copyright 2002 American Mathematical Society

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