2011/10/04 by Christopher J. Hillar, Hillar, Christopher J., Abraham Martín del Campo +1 · 1 citation
Computer Science · Mathematics · #06A07 #13E05 #13E15 #13P99 #20B30 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1110.0785
openalex publication_date 2011/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study chains of lattice ideals that are invariant under a symmetric group\naction. In our setting, the ambient rings for these ideals are polynomial rings\nwhich are increasing in (Krull) dimension. Thus, these chains will fail to\nstabilize in the traditional commutative algebra sense. However, we prove a\ntheorem which says that "up to the action of the group", these chains locally\nstabilize. We also give an algorithm, which we have implemented in software,\nfor explicitly constructing these stabilization generators for a family of\nLaurent toric ideals involved in applications to algebraic statistics. We close\nwith several open problems and conjectures arising from our theoretical and\ncomputational investigations.\n