The Longest Increasing Subsequence Problem revisited (opens in new tab)

The Longest Increasing Subsequence problem - a classic combinatorial challenge with deep connections to statistical mechanics- exhibits a rich thermodynamic landscape. Introducing a temperature we identify two distinct energy scales: A Schottky-like crossover at T_cross and a condensation transition at T_cond, below which the number of maximum-length configurations becomes sub-exponential in system size. We also show that despite the existence o...