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Immediately following the commentary below, this previously published article is reprinted in its entirety: David Aldous and Persi Diaconis, “Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem”,  Bull. Amer. Math. Soc. (N.S.)   36  (1999), no. 4, 413–432.

Commentary on “Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem” by David Aldous and Persi Diaconis