Closure relations, Buchberger's algorithm, and polynomials in infinitely many variables
Computation theory and logic
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Higher Lawrence configurations
Journal of Combinatorial Theory Series A
On the Ideals of Secant Varieties of Segre Varieties
Foundations of Computational Mathematics
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A finiteness theorem for Markov bases of hierarchical models
Journal of Combinatorial Theory Series A
Letterplace ideals and non-commutative Gröbner bases
Journal of Symbolic Computation
Viterbi sequences and polytopes
Journal of Symbolic Computation
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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.