  This is a chapter destined for the book "Handbook of the Tutte Polynomial".
The chapter is a composite. The first part is a brief introduction to
Orlik-Solomon algebras. The second part sketches the theory of evaluative
functions on matroid base polytopes and in particular, the G-invariant (as the
subject is known late 2015). A third very short section is on Hopf-algebra or
coalgebra structures in Tutte polynomial theory.
