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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Recent progress in algebraic combinatorics
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by Richard P. Stanley PDF
Bull. Amer. Math. Soc. 40 (2003), 55-68 Request permission


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
  • MR Author ID: 166285
  • Email:
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 40 (2003), 55-68
  • MSC (2000): Primary 05E99; Secondary 05E05, 14C05, 15A18, 60C05
  • DOI:
  • MathSciNet review: 1943133