On the dimension of the strongly robust complex for configurations in general position
Authors
Dimitra Kosta
Apostolos Thoma
Marius Vladoiu
Abstract
Strongly robust toric ideals are the toric ideals for which the set of indispensable binomials is the Graver basis. The strongly robust simplicial complex $Δ_T$ of a simple toric ideal $I_T$ determines the strongly robust property for all toric ideals that have $I_T$ as their bouquet ideal. We prove that $\text{dim} Δ_T<\text{rank}(T)$ for configurations in general position, partially answering a question posed by Sullivant.
