2022/08/19 by Yupeng Li, Ezra Miller, Li, Yupeng +3
Computer Science · Mathematics · #05E40 #05E45 #13C13 #13D02 #13F20 #13F65 #20M14 (Secondary) #20M25 (Primary) #68W30 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2208.09557
openalex publication_date 2022/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form combinatorial description as a sum over lattice paths in ℤn of weights that come from sequences of faces in simplicial complexes indexed by lattice points. Over a field of any characteristic, a non-canonical but simpler resolution is constructed by selecting choices of higher-dimensional analogues of spanning trees along lattice paths. These constructions generalize sylvan resolutions for monomial ideals by lifting them equivariantly to lattice modules.