  John Holte [16] introduced a family of "amazing matrices" which give the
transition probabilities of "carries" when adding a list of numbers. It was
subsequently shown that these same matrices arise in the combinatorics of the
Veronese embedding of commutative algebra [4,6,7] and in the analysis of riffle
shuffling [6,7]. We find that the left eigenvectors of these matrices form the
Foulkes character table of the symmetric group and the right eigenvectors are
the Eulerian idempotents introduced by Loday [20] in work on Hochschild
homology. The connections give new closed formulae for Foulkes characters and
allow explicit computation of natural correlation functions in the original
carries problem.
