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Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals

C.J. Hillar, A. Martin del Campo Sanchez, Journal of Symbolic Computation 50 (2013) 314–334.

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Journal Article | Published | English
Author
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.
Publishing Year
Date Published
2013-03-01
Journal Title
Journal of Symbolic Computation
Volume
50
Page
314-334
ISSN
IST-REx-ID

Cite this

Hillar CJ, Martin del Campo Sanchez A. Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals. Journal of Symbolic Computation. 2013;50:314-334. doi:10.1016/j.jsc.2012.06.006
Hillar, C. J., & Martin del Campo Sanchez, A. (2013). Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals. Journal of Symbolic Computation, 50, 314–334. https://doi.org/10.1016/j.jsc.2012.06.006
Hillar, Christopher J., and Abraham Martin del Campo Sanchez. “Finiteness Theorems and Algorithms for Permutation Invariant Chains of Laurent Lattice Ideals.” Journal of Symbolic Computation 50 (2013): 314–34. https://doi.org/10.1016/j.jsc.2012.06.006.
C. J. Hillar and A. Martin del Campo Sanchez, “Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals,” Journal of Symbolic Computation, vol. 50, pp. 314–334, 2013.
Hillar CJ, Martin del Campo Sanchez A. 2013. Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals. Journal of Symbolic Computation. 50, 314–334.
Hillar, Christopher J., and Abraham Martin del Campo Sanchez. “Finiteness Theorems and Algorithms for Permutation Invariant Chains of Laurent Lattice Ideals.” Journal of Symbolic Computation, vol. 50, Elsevier, 2013, pp. 314–34, doi:10.1016/j.jsc.2012.06.006.

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