A classification of van der Waerden complexes with linear resolution
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909525391441920 |
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| author | Hibi, Takayuki Van Tuyl, Adam |
| author_facet | Hibi, Takayuki Van Tuyl, Adam |
| contents | In 2017, Ehrenborg, Govindaiah, Park, and Readdy defined the van der Waerden complex ${\tt vdW}(n,k)$ to be the simplicial complex whose facets correspond to all the arithmetic sequences on the set $\{1,\ldots,n\}$ of a fixed length $k$. To complement a classification of the Cohen--Macaulay van der Waerden complexes obtained by Hooper and Van Tuyl in 2019, a classification of van der Waerden complexes with linear resolution is presented. Furthermore, we show that the Stanley--Reisner ring of a Cohen--Macaulay van der Waerden complex is level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A classification of van der Waerden complexes with linear resolution Hibi, Takayuki Van Tuyl, Adam Commutative Algebra Combinatorics In 2017, Ehrenborg, Govindaiah, Park, and Readdy defined the van der Waerden complex ${\tt vdW}(n,k)$ to be the simplicial complex whose facets correspond to all the arithmetic sequences on the set $\{1,\ldots,n\}$ of a fixed length $k$. To complement a classification of the Cohen--Macaulay van der Waerden complexes obtained by Hooper and Van Tuyl in 2019, a classification of van der Waerden complexes with linear resolution is presented. Furthermore, we show that the Stanley--Reisner ring of a Cohen--Macaulay van der Waerden complex is level. |
| title | A classification of van der Waerden complexes with linear resolution |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2503.03083 |