Independent Set Ultra Log Concavity is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a rank matroid on a finite ground set with . The independent set sequence of satisfies \begin{align } \left(\frac{I k(M)}{\binom{n}{k}}\right)^2 \ge \frac{I {k 1}(M)}{\binom{n}{k 1}} \frac{I {k+1}(M)}{\binom{n}{k+1}} \end{align }.