Details:
Title  Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals  Author(s)  Christopher Hillar, Abraham Martín  Type  Article in Journal  Abstract  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.  Keywords  Lattice ideal, Toric ideal, Invariant ideals, Chain stabilization, Symmetric group, Finiteness, Permutation module, Nice orderings  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717112001368 
Language  English  Journal  Journal of Symbolic Computation  Volume  50  Number  0  Pages  314  334  Year  2013  Edition  0  Translation 
No  Refereed 
No 
