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=3x10^6.
There were 3 permutations for which L_n was 3408, 1 for which 
it was 3409, and so forth.


3     3408
1     3409
1     3411
5     3412
5     3413
6     3414
6     3415
11    3416
16    3417
23    3418
12    3419
42    3420
33    3421
40    3422
49    3423
76    3424
94    3425
119   3426
105   3427
148   3428
168   3429
204   3430
216   3431
227   3432
241   3433
246   3434
297   3435
279   3436
309   3437
340   3438
357   3439
361   3440
389   3441
380   3442
383   3443
366   3444
354   3445
349   3446
358   3447
311   3448
299   3449
292   3450
296   3451
236   3452
215   3453
228   3454
208   3455
179   3456
144   3457
159   3458
140   3459
125   3460
69    3461
68    3462
61    3463
59    3464
47    3465
38    3466
39    3467
23    3468
26    3469
18    3470
22    3471
15    3472
12    3473
14    3474
3     3475
6     3476
5     3477
4     3478
5     3479
4     3480
1     3481
6     3482
1     3483
1     3484
2     3486