Lubell–Yamamoto–Meshalkin inequality

In combinatorial mathematics, the Lubell–Yamamoto–Meshalkin inequality, more commonly known as the LYM inequality, is an inequality on the sizes of sets in a Sperner family, proved by Bollobás (1965), Lubell (1966), Meshalkin (1963), and Yamamoto (1954). It is named for the initials of three of its discoverers. To include the initials of all four discoverers, it is sometimes referred to as the YBLM inequality.

This inequality belongs to the field of combinatorics of sets, and has many applications in combinatorics. In particular, it can be used to prove Sperner's theorem. Its name is also used for similar inequalities.