Let G be a matrix and M(G) be the matroid defined by linear dependence on
the set E of column vectors of G. Roughly speaking, a parcel is a subset of
pairs (f,g) of functions defined on E to an Abelian group A satisfying a
coboundary condition (that f−g is a flow over A relative to G) and a
congruence condition (that the size of the supports of f and g satisfy some
congruence condition modulo an integer). We prove several theorems of the form:
a linear combination of sizes of parcels, with coefficients roots of unity,
equals an evaluation of the Tutte polynomial of M(G) at a point
(λ−1,x−1) on the complex hyperbola $(\lambda - 1)(x-1) = |A|.