Jon A. Wellner

Values of L_n, the length of the longest increasing subsequence 
in 10^4 random permutations of {1, 2, ... , n}  for n=9x10^4.
There was 1 permutation for which L_n was 567, 1 for which 
it was 568, and so forth.

1     567
1     568
2     569
1     570
6     571
4     572
10    573
17    574
40    575
47    576
79    577
110   578
173   579
230   580
308   581
382   582
439   583
538   584
543   585
625   586
736   587
643   588
683   589
663   590
621   591
522   592
484   593
439   594
364   595
310   596
235   597
194   598
131   599
110   600
93    601
61    602
49    603
32    604
18    605
19    606
11    607
11    608
6     609
3     610
2     611
2     612
2     613