University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 Toric ideals which are determinantal 169 181 8328 10.22124/jart.2025.27189.1658 EN R. Abdolmaleki Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran R. Zaare-Nahandi Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan,Iran Journal Article 2024 04 09 Consider the polynomial ring $S=\mathbb{K}[x_1,\ldots, x_n]$ over a field $\mathbb{K}$. For any equigenerated monomial ideal $I \subset S$ with the defining ideal $J$ of the fiber cone $\F(I)$ generated by quadratic binomials, we introduce a matrix. The key observation is that the set of binomial $2$-minors of this matrix serves as a generating set for $J$. This framework in particular provides a characterization of the fiber cone for Freiman ideals, as well as offering a specific characterization for the fiber cone of sortable ideals. https://jart.guilan.ac.ir/article_8328_25af691b5af2bfc1b01cfd4cdddcf8bd.pdf