  The representation theory of the symmetric groups S_n is intimately related
to combinatorics: combinatorial objects such as Young tableaux and
combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n
tends to infinity, the structure of these combinatorial objects and algorithms
becomes complicated and it is hard to extract from them some meaningful answers
to asymptotic questions. In order to overcome these difficulties, a kind of
dual combinatorics of the representation theory of the symmetric groups was
initiated in 1990s. We will concentrate on one of its highlights: Kerov
polynomials which express characters in terms of, so called, free cumulants.
