Freiman cover ideals of unmixed bipartite graphs

Guangjun Zhu; Yakun Zhao; Yijun Cui

Freiman cover ideals of unmixed bipartite graphs

Commutative Algebra 2021-05-04 v1

Authors: Guangjun Zhu , Yakun Zhao , Yijun Cui

Abstract

An equigenerated monomial ideal $I$ in the polynomial ring $R=k[z_1,\ldots, z_n]$ is a Freiman ideal if $\mu(I^2)=\ell(I)\mu(I)-{\ell(I)\choose 2}$ where $\ell(I)$ is the analytic spread of $I$ and $\mu(I)$ is the number of minimal generators of $I$ . In this paper we classify all simple connected unmixed bipartite graphs whose cover ideals are Freiman ideals.

Keywords

freiman ideals cover ideals unmixed bipartite graphs monomial ideals analytic spread minimal generators

Cite

@article{arxiv.2105.00871,
  title  = {Freiman cover ideals of unmixed bipartite graphs},
  author = {Guangjun Zhu and Yakun Zhao and Yijun Cui},
  journal= {arXiv preprint arXiv:2105.00871},
  year   = {2021}
}

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