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PreprintCC BY 4.0arXiv

On the Hilbert Series and Multiplicity of Generalized Binomial Edge Ideals

  • Paramhans Kushwaha
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Abstract

In this article, we compute the Hilbert series of the generalized binomial edge ideal associated with the join of two graphs. Consequently, we compute the Hilbert series of complete r-partite graphs. Further, we show that if a vertex satisfies a certain degree condition, then some Hilbert coefficients remain unchanged upon its removal. This provides a reduction technique for computing them. As an application, we compute the dimension and multiplicity of several classes of graphs.

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Cite

BibTeXRIS
BibTeX
@misc{kushwaha2026hilbert,
  title = {{On the Hilbert Series and Multiplicity of Generalized Binomial Edge Ideals}},
  author = {Paramhans Kushwaha},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.12730},
  eprint = {2609.12730},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12730},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Hilbert Series and Multiplicity of Generalized Binomial Edge Ideals
AU  - Paramhans Kushwaha
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.12730
UR  - https://arxiv.org/abs/2609.12730
AB  - In this article, we compute the Hilbert series of the generalized binomial edge ideal associated with the join of two graphs. Consequently, we compute the Hilbert series of complete r-partite graphs. Further, we show that if a vertex satisfies a certain degree condition, then some Hilbert coefficients remain unchanged upon its removal. This provides a reduction technique for computing them. As an application, we compute the dimension and multiplicity of several classes of graphs.
ER  -