Young diagrams arise naturally in the theory of integer partitions.
Despite the apparent simplicity of this statement, mathematicians have not yet discovered a really easy proof. Robinson and Frame and, independently, Thrall, discovered and proved the formula on the same day in May 1953. We shall see the proof by Green, Nijenhuis and Wilf which dates from 1979. This proof uses simple probability theory and no advanced mathematics. In this section we shall only describe the algorithm.