  We introduce and study a family of inhomogeneous symmetric functions which we
call the Frobenius-Schur functions. These functions are indexed by partitions
and differ from the conventional Schur functions in lower terms only.
  Our interest in these new functions comes from the fact that they provide an
explicit expression for the dimension of a skew Young diagram in terms of the
Frobenius coordinates. This is important for the asymptotic theory of the
characters of the symmetric groups.
  Our main result is a surprisingly simple determinantal expression of the
Frobenius-Schur functions in terms of the conventional Schur functions. Other
results include certain generating series, the Giambelli formula, vanishing
properties and interpolation, a combinatorial formula (representation in terms
of tableaux), and a Sergeev-Pragacz-type formula.
  Actually, we deal with a wider class of inhomogeneous symmetric functions
which we call multiparameter Schur functions. These functions depend on an
arbitrary doubly infinite sequence of parameters and interpolate between the
Frobenius--Schur functions and the conventional Schur functions.
  This paper contains the statements of the results and the main formulas.
Proofs will be given in an expanded version of the paper which will be posted
in the arXiv.
