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=2x10^6.
There were 3 permutations for which L_n was 2778, 4 for which 
it was 2779, and so forth.


3     2778
4     2779
1     2780
3     2781
6     2782
9     2783
15    2784
23    2785
28    2786
30    2787
34    2788
54    2789
50    2790
83    2791
88    2792
106   2793
122   2794
147   2795
181   2796
194   2797
226   2798
244   2799
303   2800
327   2801
312   2802
364   2803
378   2804
375   2805
357   2806
403   2807
413   2808
397   2809
415   2810
373   2811
367   2812
378   2813
345   2814
324   2815
341   2816
279   2817
228   2818
206   2819
196   2820
155   2821
151   2822
144   2823
130   2824
129   2825
82    2826
101   2827
53    2828
62    2829
57    2830
40    2831
22    2832
19    2833
19    2834
22    2835
20    2836
15    2837
11    2838
8     2839
8     2840
3     2841
1     2842
3     2843
5     2844
1     2845
2     2847
2     2849
2     2850
1     2855