  We present positivity conjectures for the Schur expansion of Jack symmetric
functions in two bases given by binomial coefficients. Partial results suggest
that there are rich combinatorics to be found in these bases, including
Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards.
These results also lead to further conjectures about the fundamental
quasisymmetric expansions of these bases, which we prove for special cases.
