Betti Numbers of Edge Ideals of Weighted Oriented Crown Graphs
Zexin Wang, Dancheng Lu
TL;DR
This paper introduces a new method to compute multigraded Betti numbers of edge ideals in weighted oriented crown graphs, revealing that these Betti numbers are unaffected by the weight function.
Contribution
The paper presents the induced subgraph approach for calculating Betti numbers and proves their independence from weight functions in weighted oriented crown graphs.
Findings
Betti numbers are independent of weight functions
Introduces the induced subgraph approach
Calculates multigraded Betti numbers for specific graphs
Abstract
We compute the multigraded Betti numbers of edge ideals for weighted oriented crown graphs using a novel approach. This approach, which we still call the \emph{induced subgraph approach}, originates from our prior work on computing Betti numbers of normal edge rings(see \cite{WL}). Notably, we prove that the total Betti numbers of edge ideals for weighted oriented crown graphs are independent of the weight function.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Rings, Modules, and Algebras