Séminaire Lotharingien de Combinatoire, 95B.45 (2026), 12 pp.
Marie Albenque and Laurent Ménard and Nicolas Tokka
Blossoming Bijection for Bipartite Maps: a new Approach via orientations and Applications to the Ising Model
Abstract.
We develop a new bijective framework for the enumeration of bipartite planar maps with control on the degree distributions of black and white vertices. We introduce a family of orientations on bipartite maps that connects the bijection of Bousquet-Mélou and Schaeffer to the general scheme of Albenque and Poulalhon. This enables us to generalize Bousquet-Mélou and Schaeffer's bijection to several families of bipartite maps. As an application, we also derive a rational Lagrangian parametrization with positive integer coefficients for the generating series of quartic maps equipped with an Ising model.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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