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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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Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem
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by David Aldous and Persi Diaconis PDF
Bull. Amer. Math. Soc. 36 (1999), 413-432 Request permission


We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of Baik-Deift-Johansson which yields limiting probability laws via hard analysis of Toeplitz determinants.
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Additional Information
  • David Aldous
  • Affiliation: Departments of Mathematics and Statistics, Stanford University, Stanford, CA 94305
  • MR Author ID: 24555
  • Email:
  • Persi Diaconis
  • Affiliation: Departments of Mathematics and Statistics, Stanford University, Stanford, CA 94305
  • MR Author ID: 57595
  • Received by editor(s): May 17, 1999
  • Published electronically: July 21, 1999
  • Additional Notes: Research supported by NSF Grant MCS 96-22859.
  • © Copyright 1999 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 36 (1999), 413-432
  • MSC (1991): Primary 60C05, 05E10, 15A52, 60F05
  • DOI:
  • MathSciNet review: 1694204