Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913997446447104 |
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| author | Berggren, Tomas Russkikh, Marianna |
| author_facet | Berggren, Tomas Russkikh, Marianna |
| contents | This paper explores the connection between perfect t-embeddings and the octahedron equation in the setting of the two-periodic Aztec diamond. In particular, we show that the positions of both the t-embedding and the corresponding origami map can be expressed as sums of density functions arising from solutions to the octahedron equation with appropriate flat initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond Berggren, Tomas Russkikh, Marianna Mathematical Physics Combinatorics Probability 82B20 This paper explores the connection between perfect t-embeddings and the octahedron equation in the setting of the two-periodic Aztec diamond. In particular, we show that the positions of both the t-embedding and the corresponding origami map can be expressed as sums of density functions arising from solutions to the octahedron equation with appropriate flat initial conditions. |
| title | Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond |
| topic | Mathematical Physics Combinatorics Probability 82B20 |
| url | https://arxiv.org/abs/2508.06697 |