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=5x10^6.
There were 3 permutations for which L_n was 4412, 2 for which 
it was 4413, and so forth.


3     4412
2     4413
1     4414
1     4415
3     4416
7     4417
5     4418
7     4419
10    4420
13    4421
16    4422
22    4423
30    4424
26    4425
31    4426
44    4427
70    4428
71    4429
101   4430
106   4431
118   4432
116   4433
117   4434
169   4435
203   4436
207   4437
223   4438
231   4439
273   4440
303   4441
312   4442
300   4443
302   4444
333   4445
323   4446
311   4447
383   4448
335   4449
313   4450
342   4451
331   4452
284   4453
301   4454
318   4455
272   4456
270   4457
235   4458
222   4459
186   4460
199   4461
182   4462
164   4463
158   4464
141   4465
131   4466
99    4467
93    4468
106   4469
66    4470
67    4471
47    4472
45    4473
46    4474
34    4475
44    4476
34    4477
27    4478
12    4479
20    4480
10    4481
16    4482
15    4483
10    4484
5     4485
5     4486
2     4487
4     4488
4     4489
2     4491
1     4492
1     4493
2     4494
2     4495
3     4498
1     4502