Double boxes and double dimers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929698817179648 |
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| author | Benko, Tatyana Young, Benjamin |
| author_facet | Benko, Tatyana Young, Benjamin |
| contents | We give a combinatorial proof of a result in rank 2 Donaldson-Thomas theory, which states that the generating function for certain plane-partition-like objects, called double-box configurations, is equal to a product of MacMahon's generating function for (boxed) plane partitions. In our proof, we first give the correspondence between double-box configurations and double-dimer configurations on the hexagon lattice with a particular tripartite node pairing. Using this correspondence, we apply graphical condensation and double-dimer condensation to prove the result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Double boxes and double dimers Benko, Tatyana Young, Benjamin Combinatorics We give a combinatorial proof of a result in rank 2 Donaldson-Thomas theory, which states that the generating function for certain plane-partition-like objects, called double-box configurations, is equal to a product of MacMahon's generating function for (boxed) plane partitions. In our proof, we first give the correspondence between double-box configurations and double-dimer configurations on the hexagon lattice with a particular tripartite node pairing. Using this correspondence, we apply graphical condensation and double-dimer condensation to prove the result. |
| title | Double boxes and double dimers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.02980 |