2018/12/05 by Maria Barouti, Barouti, Maria
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1812.01757
openalex publication_date 2018/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One standard approach to compute the Hilbert function of any graded module over a field is to come up with a free-resolution for the graded module and another is via a Hilbert power series which serves as a generating function. The proposed approaches enable generating the values of a Hilbert function when the graded module is a quotient ring over a field by using combinatorics and homological algebra. Two of these approaches named the lcm-Lattice method and the Syzygy method, are conceptually combinatorial and work for any polynomial quotient ring over a field. The third approach named Hilbert function table method, also uses syzygies but the approach is better described in terms of homological algebra.