We study chains of lattice ideals that are invariant under a symmetric group action. In our setting, the ambient rings for these ideals are polynomial rings which are increasing in (Krull) dimension. Thus, these chains will fail to stabilize in the traditional commutative algebra sense. However, we prove a theorem which says that ”up to the action of the group”, these chains locally stabilize. We also give an algorithm, which we have implemented in software, for explicitly constructing these stabilization generators for a family of Laurent toric ideals involved in applications to algebraic statistics. We close with several open problems and conjectures arising from our theoretical and computational investigations
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References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Hillar, Christopher J.; del Campo, Abraham Martín: Corrigendum to: “Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals” (2016)
- da Costa, E.A.; Krasilnikov, A.: Symmetric polynomials and nonfinitely generated $\mathrmSym(\mathbbN)$-invariant ideals (2015)
- Hillar, Christopher J.; del Campo, Abraham Martín: Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals (2013)
- Michałek, Mateusz: Constructive degree bounds for group-based models (2013)