A new formula for an evaluation of the Tutte polynomial of a matroid

Given a matroid M and its Tutte polynomial image, image is an invariant of M with various interesting combinatorial and topological interpretations. Being a Tutte–Grothendieck invariant, image may be computed via deletion–contraction recursions. In this note we derive a new recursion formula for this invariant that involves contractions of M through the circuits containing a fixed element of M.