On the combinatorics of the refined 1-leg DT/PT correspondence
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917381824053248 |
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| author | Accadia, Davide Lewański, Danilo Monavari, Sergej |
| author_facet | Accadia, Davide Lewański, Danilo Monavari, Sergej |
| contents | We provide a new proof of a result of Bessenrodt on the relation among the generating series of reversed plane partitions and skew plane partitions, motivated by the geometric DT/PT wallcrossing formula for local curves recently proved by the third author. This also recovers a result of Sagan.
We moreover establish various new closed formulas for the weighted enumeration of reversed and skew plane partitions, proving a result dual to a theorem by Gansner, we find a new identity on the generating series counting internal and external hooks of a given Young diagram, and we combine the latter with Bessenrodt's theorem. Finally, we interpret our results as identities in the Fock space via the bosonic/fermionic formalism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_29435 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the combinatorics of the refined 1-leg DT/PT correspondence Accadia, Davide Lewański, Danilo Monavari, Sergej Combinatorics Algebraic Geometry 05A19 (Primary), 14N35 (Secondary) We provide a new proof of a result of Bessenrodt on the relation among the generating series of reversed plane partitions and skew plane partitions, motivated by the geometric DT/PT wallcrossing formula for local curves recently proved by the third author. This also recovers a result of Sagan. We moreover establish various new closed formulas for the weighted enumeration of reversed and skew plane partitions, proving a result dual to a theorem by Gansner, we find a new identity on the generating series counting internal and external hooks of a given Young diagram, and we combine the latter with Bessenrodt's theorem. Finally, we interpret our results as identities in the Fock space via the bosonic/fermionic formalism. |
| title | On the combinatorics of the refined 1-leg DT/PT correspondence |
| topic | Combinatorics Algebraic Geometry 05A19 (Primary), 14N35 (Secondary) |
| url | https://arxiv.org/abs/2603.29435 |