  We consider Blanchet, Habegger, Masbaum and Vogel's universal construction of
topological theories in dimension two, using it to produce interesting theories
that do not satisfy the usual two-dimensional TQFT axioms. Kronecker's
characterization of rational functions allows us to classify theories over a
field with finite-dimensional state spaces and introduce their extension to
theories with the ground ring the product of rings of symmetric functions in N
and M variables. We look at several examples of non-multiplicative theories and
see Hankel matrices, Schur and supersymmetric Schur polynomials quickly emerge
from these structures. The last section explains how an extension of the
Robert-Wagner foam evaluation to overlapping foams gives the Sergeev-Pragacz
formula for the supersymmetric Schur polynomials and the Day formula for the
Toeplitz determinant of rational power series as special cases.
