Eulerian orientations and the six-vertex model on planar map
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866916681507405824 |
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| author | Bousquet-Mélou, Mireille Price, Andrew Elvey Zinn-Justin, Paul |
| author_facet | Bousquet-Mélou, Mireille Price, Andrew Elvey Zinn-Justin, Paul |
| contents | We address the enumeration of planar 4-valent maps equipped with an Eulerian orientation by two different methods, and compare the solutions we thus obtain. With the first method we enumerate these orientations as well as a restricted class which we show to be in bijection with general Eulerian orientations. The second method, based on the work of Kostov, allows us to enumerate these 4-valent orientations with a weight on some vertices, corresponding to the six vertex model. We prove that this result generalises both results obtained using the first method, although the equivalence is not immediately clear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_07369 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Eulerian orientations and the six-vertex model on planar map Bousquet-Mélou, Mireille Price, Andrew Elvey Zinn-Justin, Paul Combinatorics We address the enumeration of planar 4-valent maps equipped with an Eulerian orientation by two different methods, and compare the solutions we thus obtain. With the first method we enumerate these orientations as well as a restricted class which we show to be in bijection with general Eulerian orientations. The second method, based on the work of Kostov, allows us to enumerate these 4-valent orientations with a weight on some vertices, corresponding to the six vertex model. We prove that this result generalises both results obtained using the first method, although the equivalence is not immediately clear. |
| title | Eulerian orientations and the six-vertex model on planar map |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1902.07369 |