Flat Flag Description of the Bergman Fan is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a loopless matroid on a finite ground set , and let denote the Bergman fan defined by the circuit condition \begin{align } \widetilde{\mathcal B}(M)=\{w \in \mathbb{R}^E : \text{for every circuit } C \text{ of } M,\ \min {e \in C} w.