tuttePolynomial M
The Tutte polynomial is an invariant of a matroid that is universal with respect to satisfying a deletioncontraction recurrence. Indeed, one way to define the Tutte polynomial of a matroid is: if $M$ is a matroid consisting of $a$ loops and $b$ coloops, then $T_M(x, y) = x^ay^b$, and if $e \in M$ is neither a loop nor a coloop, then $T_M(x, y) := T_{M \backslash e}(x, y) + T_{M/e}(x, y)$, where M\e is the deletion of M with respect to $\{e\}$, and M/e is the contraction of M with respect to $\{e\}$. Many invariants of a matroid can be determined by substituting values into its Tutte polynomial  cf. tutteEvaluate.

