2000/03/16 by Jan Snellman, Snellman, Jan
Computer Science · Mathematics · #13D40 #13P10 #Advanced Optimization Algorithms Research #Algebraic and Geometric Analysis #Commutative Algebra (math.AC) #FOS: Mathematics #Matrix Theory and Algorithms #math.AC #msc:13D40 #msc:13P10
paper · pdf · doi:10.48550/arxiv.math/0003097
19 pages, LaTeX2e
arxiv created 2000/03/16 · openalex publication_date 2000/03/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We associate to each r-multigraded, locally finitely generated ideal in the "large polynomial ring" on countably many indeterminates a power series in r variables; this power series is the limit in the adic topology of the numerators of the rational functions which give the Hilbert series of the truncations of the ideal. We characterise the set of all power series so obtained. Our main technical tools are an approximation result which asserts that truncation and the forming of initial ideals commute in a filtered sense, and standard inclusion/exclusion, Möbius inversion, and LCM-lattice homology methods generalised to monomial ideals in countably many variables.