Density of linearity index in the interval of matching numbers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909554388762624 |
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| author | Erey, Nursel Hibi, Takayuki |
| author_facet | Erey, Nursel Hibi, Takayuki |
| contents | Given integers $2 \leq p \leq c \leq q$, we construct a finite simple graph $G$ with $ν_1(G) = p$ and $ν(G) = q$ for which the squarefree power $I(G)^{[k]}$ of the edge ideal $I(G)$ of $G$ has linear quotients for each $c \leq k \leq q$ and is not linearly related for each $1 \leq k < c$, where $ν_1(G)$ is the induced matching number of $G$ and $ν(G)$ is the matching number of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density of linearity index in the interval of matching numbers Erey, Nursel Hibi, Takayuki Commutative Algebra Combinatorics Given integers $2 \leq p \leq c \leq q$, we construct a finite simple graph $G$ with $ν_1(G) = p$ and $ν(G) = q$ for which the squarefree power $I(G)^{[k]}$ of the edge ideal $I(G)$ of $G$ has linear quotients for each $c \leq k \leq q$ and is not linearly related for each $1 \leq k < c$, where $ν_1(G)$ is the induced matching number of $G$ and $ν(G)$ is the matching number of $G$. |
| title | Density of linearity index in the interval of matching numbers |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2503.21008 |