The units of a partial Burnside ring relative to the Young subgroups of a symmetric group

The unit group of a partial Burnside ring relative to the Young subgroups of the symmetric group Sn on n letters is included in the image by the tom Dieck homomorphism. As a consequence of this fact, the alternating character νn of Sn is expressed explicitly as a Z-linear combinations of permutation characters associated with finite left Sn-sets Sn/Y for the Young subgroups Y.