  Given natural numbers m and n, we define a deflation map from the characters
of the symmetric group S_{mn} to the characters of S_n. This map is obtained by
first restricting a character of S_{mn} to the wreath product S_m \wr S_n, and
then taking the sum of the irreducible constituents of the restricted character
on which the base group S_m \times ... \times S_m acts trivially. We prove a
combinatorial formula which gives the values of the images of the irreducible
characters of S_{mn} under this map. We also prove an analogous result for more
general deflation maps in which the base group is not required to act
trivially. These results generalize the Murnaghan--Nakayama rule and special
cases of the Littlewood--Richardson rule. As a corollary we obtain a new
combinatorial formula for the character multiplicities that are the subject of
the long-standing Foulkes' Conjecture. Using this formula we verify Foulkes'
Conjecture in some new cases.
