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BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 36, Number 4, Pages 413432
S 0273-0979(99)00796-X
Article electronically published on July 21, 1999
LONGEST INCREASING SUBSEQUENCES: FROM PATIENCE
SORTING TO THE BAIK-DEIFT-JOHANSSON THEOREM
DAVID ALDOUS AND PERSI DIACONIS
Abstract. 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 correspon-
dence. A recent highlight of this area is the work of Baik-Deift-Johansson
which yields limiting probability laws via hard analysis of Toeplitz determi-
nants.
1. Introduction
This survey paper treats two themes in parallel. One theme is a purely math-
ematical question: describe the asymptotic law (probability distribution) of the
length of the longest increasing subsequence of a random permutation. This ques-
tion has been studied by a variety of increasingly technically sophisticated methods
over the last 30 years. We outline three, apparently quite unrelated, methods in

  

Source: Aldous, David J. - Department of Statistics, University of California at Berkeley

 

Collections: Mathematics