Betti numbers of normal edge rings (II)
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908355323232256 |
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| author | Wang, Zexin Lu, Dancheng |
| author_facet | Wang, Zexin Lu, Dancheng |
| contents | We compute the Betti numbers of the edge rings of multi-path graphs using the \emph{induced-subgraph approach} introduced in \cite{WL1}. Here, a multi-path graph refers to a simple graph composed of several paths that have the same starting point and the same ending point. Special cases include the graph $G_{r,d}$ introduced in \cite{GHK}, the graph $G_{r,s,d}$ introduced in \cite{NN}, and the graph $B_{\underline{\ell},h}$ introduced in \cite{LZ}. In particular, we show that all the multi-graded Betti numbers of a multi-path graph are the top multi-graded Betti numbers of some of its induced subgraphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_03171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Betti numbers of normal edge rings (II) Wang, Zexin Lu, Dancheng Commutative Algebra 13A02, 05E40(Primary) 06D50(Secondary) We compute the Betti numbers of the edge rings of multi-path graphs using the \emph{induced-subgraph approach} introduced in \cite{WL1}. Here, a multi-path graph refers to a simple graph composed of several paths that have the same starting point and the same ending point. Special cases include the graph $G_{r,d}$ introduced in \cite{GHK}, the graph $G_{r,s,d}$ introduced in \cite{NN}, and the graph $B_{\underline{\ell},h}$ introduced in \cite{LZ}. In particular, we show that all the multi-graded Betti numbers of a multi-path graph are the top multi-graded Betti numbers of some of its induced subgraphs. |
| title | Betti numbers of normal edge rings (II) |
| topic | Commutative Algebra 13A02, 05E40(Primary) 06D50(Secondary) |
| url | https://arxiv.org/abs/2503.03171 |