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

Given a matroid M and its Tutte polynomial T_M(x,y), T_M(0,1) is an invariant of M with various interesting combinatorial and topological interpretations. Being a Tutte–Grothendieck invariant, T_M(0,1) 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.