4 problems

Let $n$ be even, let $K_n$ be the complete graph on $n$ people with independent uniformly random preference lists, and let $X$ be the number of stable matchings. Mertens' conjectur…

An instance of the stable roommates problem consists of an even number $n$ of people, each with a ranked list of preferences over the other people, and asks whether there is a stab…

Let $n$ be even, let $K_n$ be the complete graph on $n$ people, and let each person choose an independent uniformly random strict preference ordering of the other $n-1$ people. Let…

Let $p_n$ denote the probability that a random instance of the stable roommates problem with $n$ agents admits a stable matching. Conjecture. The probability satisfies … This conje…