  Specializing the $\gamma$-basis for the vector space $\mathcal{G}(n,r)$
spanned by the set of symbols on bit sequences with $r$ $1$'s and $n-r$ $0$'s,
we obtain a frame or spanning set for the vector space $\mathcal{T}(n,r)$
spanned by Tutte polynomials of matroids having rank $r$ and size $n$. Every
Tutte polynomial can be expanded as a linear combination with non-negative
integer coefficients of elements in this frame. We give explicit formulas for
the elements in this frame. These formulas combine to give an expansion of the
Tutte polynomial with coefficients obtained by summing numerical invariants
over all flats with a given rank and size.
