  Stanley considered suitably normalized characters of the symmetric groups on
Young diagrams having a special geometric form, namely multirectangular Young
diagrams. He proved that the character is a polynomial in the lengths of the
sides of the rectangles forming the Young diagram and he conjectured an
explicit form of this polynomial. This Stanley character polynomial and this
way of parametrizing the set of Young diagrams turned out to be a powerful tool
for several problems of the dual combinatorics of the characters of the
symmetric groups and asymptotic representation theory, in particular to Kerov
polynomials.
