The number of Pfaffian orientations on punctured polygonally cellulated surfaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910247796342784 |
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| author | Mukherjee, Sajal Pramanik, Pritam Chandra Rakshit, Arundhati |
| author_facet | Mukherjee, Sajal Pramanik, Pritam Chandra Rakshit, Arundhati |
| contents | In this paper, we introduce the notion of Pfaffian orientations on (punctured) polygonally cellulated orientable surfaces, and provide an expression for the number of such orientations. This generalizes the notion of Pfaffian orientations on planar graph, where a planar graph is seen as a punctured $2$-sphere, embedded in $\mathbb{R}^3$. So, as a direct corollary of our main theorem, we derive the number of Pfaffian orientations on a planar graph. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_23548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The number of Pfaffian orientations on punctured polygonally cellulated surfaces Mukherjee, Sajal Pramanik, Pritam Chandra Rakshit, Arundhati Combinatorics 05C10, 52B05, 05A15 In this paper, we introduce the notion of Pfaffian orientations on (punctured) polygonally cellulated orientable surfaces, and provide an expression for the number of such orientations. This generalizes the notion of Pfaffian orientations on planar graph, where a planar graph is seen as a punctured $2$-sphere, embedded in $\mathbb{R}^3$. So, as a direct corollary of our main theorem, we derive the number of Pfaffian orientations on a planar graph. |
| title | The number of Pfaffian orientations on punctured polygonally cellulated surfaces |
| topic | Combinatorics 05C10, 52B05, 05A15 |
| url | https://arxiv.org/abs/2605.23548 |