A Novel Approach for Computing Hilbert Functions

Maria Barouti

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arXiv · 1812.01757

A Novel Approach for Computing Hilbert Functions

Maria Barouti

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Abstract

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.

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Maria Barouti. 2018-12-05. A Novel Approach for Computing Hilbert Functions. https://arxiv.org/abs/1812.01757

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