# log-concave

## Rota's unimodal conjecture ★★★

Author(s): Rota

Let $M$ be a matroid of rank $r$, and for $0 \le i \le r$ let $w_i$ be the number of closed sets of rank $i$.

\begin{conjecture} $w_0,w_1,\ldots,w_r$ is unimodal. \end{conjecture}

\begin{conjecture} $w_0,w_1,\ldots,w_r$ is log-concave. \end{conjecture}

Keywords: flat; log-concave; matroid