Minimal systems of binomial generators and the indispensable complex of a toric ideal

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dc.creatorCharalambous, Hara
dc.creatorKatsabekis, Anargyros
dc.creatorThoma, Apostolos
dc.date2006-07-11
dc.date.accessioned2026-07-07T07:18:14Z
dc.date.available2026-07-07T07:18:14Z
dc.descriptionLet $A=\{{\bf a}_1,...,{\bf a}_m\} \subset \mathbb{Z}^n$ be a vector configuration and $I_A \subset K[x_1,...,x_m]$ its corresponding toric ideal. The paper consists of two parts. In the first part we completely determine the number of different minimal systems of binomial generators of $I_A$. We also prove that generic toric ideals are generated by indispensable binomials. In the second part we associate to $A$ a simplicial complex $Δ_{\ind(A)}$. We show that the vertices of $Δ_{\ind(A)}$ correspond to the indispensable monomials of the toric ideal $I_A$, while one dimensional facets of $Δ_{\ind(A)}$ with minimal binomial $A$-degree correspond to the indispensable binomials of $I_{A}$.
dc.identifierhttps://arxiv.org/abs/math/0607249
dc.identifierhttp://arxiv.org/abs/math/0607249
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114225
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject13F20; 05C99
dc.titleMinimal systems of binomial generators and the indispensable complex of a toric ideal
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