**Monte Carlo computations of the distribution of lengths of longest increasing subsequences in random permutations**. [n = 10^4] [n = 10^5] [n = 10^6] [n = 10^7] [n = 10^8] [n = 10^9] [n = 10^10]**Exact distribution of lengths of longest increasing subsequences in permutations**. [n = 15] [n = 30] [n = 60] [n = 90] [n = 120]