Values of L_n, the length of the longest increasing subsequence in 10^4 random permutations of {1, 2, ... , n} for n=6x10^3. There was 1 permutation for which L_n was 135, 2 for which it was 136, and so forth. 1 135 2 136 5 137 13 138 38 139 82 140 188 141 295 142 488 143 655 144 846 145 1054 146 1111 147 1024 148 994 149 833 150 725 151 557 152 393 153 282 154 182 155 96 156 58 157 44 158 15 159 7 160 7 161 2 162 2 163 1 164