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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.03680 |
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| _version_ | 1866914140959801344 |
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| author | Albenque, Marie Ménard, Laurent Tokka, Nicolas |
| author_facet | Albenque, Marie Ménard, Laurent Tokka, Nicolas |
| contents | We develop a new bijective framework for the enumeration of bipartite planar maps with control on the degree distribution of black and white vertices. Our approach builds on the blossoming-tree paradigm, introducing a family of orientations on bipartite maps that extends Eulerian and quasi-Eulerian orientations and connects the bijection of Bousquet-Mélou and Schaeffer to the general scheme of Albenque and Poulalhon. This enables us to generalize the Bousquet-Mélou and Schaeffer's bijection to several families of bipartite maps.
As an application, we also derive a rational and Lagrangian parametrization with positive integer coefficients for the generating series of quartic maps equipped with an Ising model, which is key to the probabilistic study of these maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blossoming bijection for bipartite maps: a new approach via orientations and applications to the Ising model Albenque, Marie Ménard, Laurent Tokka, Nicolas Combinatorics Mathematical Physics We develop a new bijective framework for the enumeration of bipartite planar maps with control on the degree distribution of black and white vertices. Our approach builds on the blossoming-tree paradigm, introducing a family of orientations on bipartite maps that extends Eulerian and quasi-Eulerian orientations and connects the bijection of Bousquet-Mélou and Schaeffer to the general scheme of Albenque and Poulalhon. This enables us to generalize the Bousquet-Mélou and Schaeffer's bijection to several families of bipartite maps. As an application, we also derive a rational and Lagrangian parametrization with positive integer coefficients for the generating series of quartic maps equipped with an Ising model, which is key to the probabilistic study of these maps. |
| title | Blossoming bijection for bipartite maps: a new approach via orientations and applications to the Ising model |
| topic | Combinatorics Mathematical Physics |
| url | https://arxiv.org/abs/2511.03680 |