Bulletin of the American Mathematical Society

Author(s): Richard P. Stanley
Journal: Bull. Amer. Math. Soc. 40 (2003), 55-68.
MSC (2000): Primary 05E99; Secondary 05E05, 14C05, 15A18, 60C05
Posted: October 11, 2002
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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

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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