A case study of Gr\"obner bases and Hilbert series
Soutrik Roy Chowdhury
TL;DR
This paper introduces Gr"obner bases and demonstrates their application in computing Hilbert series for certain algebraic structures, providing illustrative examples and computational techniques.
Contribution
It offers an accessible exposition on Gr"obner bases and their use in calculating Hilbert series for chain-based algebras, with practical computations included.
Findings
Computed Gr"obner bases for specific algebras
Demonstrated Hilbert series calculation methods
Provided illustrative examples for algebraic computations
Abstract
In this expository style of writing I will give an introduction of Gr\"{o}bner bases and compute it for some algebras and then show how to use it to compute Hilbert series for algebras from chains.
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Taxonomy
TopicsAdvanced Algebra and Logic · Commutative Algebra and Its Applications · Polynomial and algebraic computation