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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.24196 |
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| _version_ | 1866914247205715968 |
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| author | Lin, Yijie |
| author_facet | Lin, Yijie |
| contents | We introduce a notion of restricted pyramid configurations for computing the 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex. We study a special type of restricted pyramid configurations with the prescribed 1-leg partitions, and find one unique class of them satisfying the symmetric interlacing property. This leads us to obtain an explicit formula for a class of 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex through establishing its connection with 1-leg Donaldson-Thomas $\mathbb{Z}_4$-vertex using the vertex operator methods of Okounkov-Reshetikhin-Vafa and Bryan-Young. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex Lin, Yijie Algebraic Geometry We introduce a notion of restricted pyramid configurations for computing the 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex. We study a special type of restricted pyramid configurations with the prescribed 1-leg partitions, and find one unique class of them satisfying the symmetric interlacing property. This leads us to obtain an explicit formula for a class of 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex through establishing its connection with 1-leg Donaldson-Thomas $\mathbb{Z}_4$-vertex using the vertex operator methods of Okounkov-Reshetikhin-Vafa and Bryan-Young. |
| title | On the 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.24196 |