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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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Table of 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.