Bijectivizing the PT-DT Correspondence
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910732448169984 |
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| author | Godar, Cruz Young, Benjamin |
| author_facet | Godar, Cruz Young, Benjamin |
| contents | Pandharipande-Thomas theory and Donaldson-Thomas theory (PT and DT) are two branches of enumerative geometry in which particular generating functions arise that count plane-partition-like objects. That these generating functions differ only by a factor of MacMahon's function was proven recursively by Jenne, Webb, and Young using the double dimer model. We bijectivize two special cases of the result by formulating these generating functions using vertex operators and applying a particular type of local involution known as a toggle, first introduced in the form we use by Pak. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_09920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bijectivizing the PT-DT Correspondence Godar, Cruz Young, Benjamin Combinatorics 05A19 Pandharipande-Thomas theory and Donaldson-Thomas theory (PT and DT) are two branches of enumerative geometry in which particular generating functions arise that count plane-partition-like objects. That these generating functions differ only by a factor of MacMahon's function was proven recursively by Jenne, Webb, and Young using the double dimer model. We bijectivize two special cases of the result by formulating these generating functions using vertex operators and applying a particular type of local involution known as a toggle, first introduced in the form we use by Pak. |
| title | Bijectivizing the PT-DT Correspondence |
| topic | Combinatorics 05A19 |
| url | https://arxiv.org/abs/2411.09920 |