symmChainGens swMATH ID: 6689 Software Authors: Hillar, Christopher J.; Del Campo, Abraham Martín Description: 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 Homepage: http://pub.ist.ac.at/~adelcampo/Files/Code/symmChainGens.m2 Dependencies: Macaulay2 Related Software: FourTiTwo; 4ti2; PieriMaps; Letterplace; LDA; Janet; Maple; SINGULAR; Macaulay2 Cited in: 8 Publications all top 5 Cited by 8 Authors 2 del Campo, Abraham Martín 2 Hillar, Christopher J. 2 Sam, Steven V. 2 Snowden, Andrew W. 1 La Scala, Roberto 1 Le, Dinh Van 1 Michałek, Mateusz 1 Römer, Tim all top 5 Cited in 7 Serials 2 Journal of Symbolic Computation 1 Discrete Mathematics 1 Mathematics of Computation 1 Journal of Combinatorial Theory. Series A 1 Transactions of the American Mathematical Society 1 Journal of the American Mathematical Society 1 Journal of Mathematical Sciences (New York) all top 5 Cited in 8 Fields 6 Commutative algebra (13-XX) 3 Combinatorics (05-XX) 3 Algebraic geometry (14-XX) 2 Associative rings and algebras (16-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Computer science (68-XX) 1 Biology and other natural sciences (92-XX) Citations by Year