Algebra and valuations related to the Tutte polynomial

Abstract

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.