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TitleFiniteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals
Author(s) Christopher Hillar, Abraham Martín
TypeArticle in Journal
AbstractWe 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.
KeywordsLattice ideal, Toric ideal, Invariant ideals, Chain stabilization, Symmetric group, Finiteness, Permutation module, Nice orderings
URL http://www.sciencedirect.com/science/article/pii/S0747717112001368
JournalJournal of Symbolic Computation
Pages314 - 334
Translation No
Refereed No