The amoeba dimension of a linear space.

Given a complex vector subspace V of \mathbb {C}^n, the dimension of the amoeba of V \cap (\mathbb {C}^*)^n depends only on the matroid that V defines on the ground set \{1,\ldots,n\}. Here we prove that this dimension is given by the minimum of a certain function over all partitions of the ground set, as previously conjectured by Rau. We also prove that this formula can be evaluated in polynomial time. [ABSTRACT FROM AUTHOR]