Plane partitions and spin adapted quantum states
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918281186639872 |
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| author | Price, Abigail Stelzer, Ada Sverrisdóttir, Svala |
| author_facet | Price, Abigail Stelzer, Ada Sverrisdóttir, Svala |
| contents | We describe an explicit basis for the $\operatorname{SU}(2)$-invariant space of the exterior power $\wedge_{2k} \mathbb{C}^{2m}$ via the combinatorics of plane partitions. In quantum chemistry, this is the space of spin adapted quantum states of an electronic system with $m$ spin orbitals and $k$ electron pairs. We construct our basis by identifying the invariant space with an Artinian commutative ring called the excitation ring. We compute a Gröbner basis and enumerate its standard monomials via an explicit bijection to Dyck paths counted by the Narayana numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_06295 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Plane partitions and spin adapted quantum states Price, Abigail Stelzer, Ada Sverrisdóttir, Svala Combinatorics Commutative Algebra Chemical Physics We describe an explicit basis for the $\operatorname{SU}(2)$-invariant space of the exterior power $\wedge_{2k} \mathbb{C}^{2m}$ via the combinatorics of plane partitions. In quantum chemistry, this is the space of spin adapted quantum states of an electronic system with $m$ spin orbitals and $k$ electron pairs. We construct our basis by identifying the invariant space with an Artinian commutative ring called the excitation ring. We compute a Gröbner basis and enumerate its standard monomials via an explicit bijection to Dyck paths counted by the Narayana numbers. |
| title | Plane partitions and spin adapted quantum states |
| topic | Combinatorics Commutative Algebra Chemical Physics |
| url | https://arxiv.org/abs/2601.06295 |