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===== Stable Matchings =====
For a basic definition of what a stable matching is, see [[https://en.wikipedia.org/wiki/Stable_marriage_problem|Wikipedia]].

==== Lattice structure ===
The set of stable matchings has a nice combinatorial structure.
To learn more about it, I recommend this awesome [[https://mitpress.mit.edu/books/stable-marriage-problem|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: 
  * [[https://www.irif.fr/~mauras/stablematchings/1|Instance used in Gusfield and Irving's book]]
  * [[https://www.irif.fr/~mauras/stablematchings/2|Instance with an unbalanced number of persons]]
  * [[https://www.irif.fr/~mauras/stablematchings/3|Instance of size 10 where every pair belong to a stable matching]]
  * [[https://www.irif.fr/~mauras/stablematchings/4|Instance of size 10 with 5 independent rotations]]
  * [[https://www.irif.fr/~mauras/stablematchings/5|Instance of size 10 with preferences generated uniformly at random]]
  * [[https://www.irif.fr/~mauras/stablematchings/6|Instance of size 5 where every pair belong to a stable matching]]
  * [[https://www.irif.fr/~mauras/stablematchings/7|Instance of size 8 maximizing the number of stable matchings]]
  * [[https://www.irif.fr/~mauras/stablematchings/8|Instance of size 20 with preferences generated uniformly at random]]

The code used to generate those animations is available on [[https://github.com/simon-mauras/stable-matchings|GitHub]].