This page is under construction… More content will be added later. Stable Matchings For a basic definition of what a stable matching is, see Wikipedia. Lattice structure The set of stable matchings has a nice combinatorial structure. To learn more about it, I recommend this awesome book written by Gusfield and Irving. To see what the lattice of stable matchings looks like on small examples, have a look at the following animations: Instance used in Gusfield and Irving's book Instance with an unbalanced number of persons Instance of size 10 where every pair belong to a stable matching Instance of size 10 with 5 independent rotations Instance of size 10 with preferences generated uniformly at random Instance of size 5 where every pair belong to a stable matching Instance of size 8 maximizing the number of stable matchings Instance of size 20 with preferences generated uniformly at random The code used to generate those animations is available on GitHub.