The table of marks, the Kostka matrix, and the character table of the symmetric group

In this article, we introduce a short proof of T=KCT=KC, where T is the table of marks with respect to the Young subgroups, K is the Kostka matrix, and C   is the character table of the symmetric group SnSn. As a corollary of the result, we could determine the explicit elements of the unit group of the generalized Burnside ring with respect to the Young subgroups of SnSn.