A note on toric ideals of graphs and Knutson-Miller-Yong decompositions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917919595692032 |
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| author | Da Silva, Sergio Naguit, Emma Rajchgot, Jenna |
| author_facet | Da Silva, Sergio Naguit, Emma Rajchgot, Jenna |
| contents | We use a Gröbner basis technique first introduced by Knutson, Miller and Yong to study the interplay between properties of a graph $G$ and algebraic properties of the toric ideal that it defines. We first recover a well-known height formula for the toric ideal of a graph $I_G$ and demonstrate an algebraic property that can detect when a graph deletion is bipartite. We also bound the chromatic number $χ(G)$ using information about an initial ideal of $I_G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on toric ideals of graphs and Knutson-Miller-Yong decompositions Da Silva, Sergio Naguit, Emma Rajchgot, Jenna Commutative Algebra Combinatorics 13P10, 14M25, 05C15, 05E40, 05C25 We use a Gröbner basis technique first introduced by Knutson, Miller and Yong to study the interplay between properties of a graph $G$ and algebraic properties of the toric ideal that it defines. We first recover a well-known height formula for the toric ideal of a graph $I_G$ and demonstrate an algebraic property that can detect when a graph deletion is bipartite. We also bound the chromatic number $χ(G)$ using information about an initial ideal of $I_G$. |
| title | A note on toric ideals of graphs and Knutson-Miller-Yong decompositions |
| topic | Commutative Algebra Combinatorics 13P10, 14M25, 05C15, 05E40, 05C25 |
| url | https://arxiv.org/abs/2502.08069 |