The $n$-Point Function of $t$-Core Partitions and Topological Vertex
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914478946254848 |
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| author | Yang, Chenglang |
| author_facet | Yang, Chenglang |
| contents | In this paper, we study the $n$-point function of $t$-core partitions. The main tool is the topological vertex, originally developed to study the topological string theory for toric Calabi--Yau 3-folds. By virtue of the topological vertex, we introduce the $q$-deformed $n$-point function that generalizes both the ordinary $n$-point function of all integer partitions studied by Bloch--Okounkov and $t$-core partition case treated here. As a consequence, we provide a closed formula for the $n$-point function of $t$-core partitions in terms of theta functions, and prove that the corresponding correlation functions are quasimodular forms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14542 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $n$-Point Function of $t$-Core Partitions and Topological Vertex Yang, Chenglang Mathematical Physics Combinatorics Quantum Algebra Representation Theory In this paper, we study the $n$-point function of $t$-core partitions. The main tool is the topological vertex, originally developed to study the topological string theory for toric Calabi--Yau 3-folds. By virtue of the topological vertex, we introduce the $q$-deformed $n$-point function that generalizes both the ordinary $n$-point function of all integer partitions studied by Bloch--Okounkov and $t$-core partition case treated here. As a consequence, we provide a closed formula for the $n$-point function of $t$-core partitions in terms of theta functions, and prove that the corresponding correlation functions are quasimodular forms. |
| title | The $n$-Point Function of $t$-Core Partitions and Topological Vertex |
| topic | Mathematical Physics Combinatorics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2604.14542 |