Values of L_n, the length of the longest increasing subsequence in 10^4 random permutations of {1, 2, ... , n} for n=5x10^3. There was 1 permutation for which L_n was 123, 2 for which it was 124, and so forth. 1 123 2 124 21 125 30 126 103 127 188 128 344 129 524 130 751 131 967 132 1065 133 1113 134 1084 135 989 136 844 137 620 138 481 139 314 140 227 141 151 142 87 143 48 144 26 145 8 146 5 147 4 148 3 149