3 papers
math.CO2026
A tree bijection for Eulerian orientations on quartic maps
Marie Albenque, Enrica Duchi, Juliette Schabanel
In this paper we construct a recursive bijection between -valent maps endowed with a Eulerian orientation -- also known as the ice model -- and a family of unary-binary trees. T…
math.CO2025
Blossoming bijection for bipartite maps: a new approach via orientations and applications to the Ising model
Marie Albenque, Laurent Ménard, Nicolas Tokka
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 bl…
math.CO2025
The slice decomposition of planar hypermaps
Marie Albenque, Jérémie Bouttier
The slice decomposition is a bijective method for enumerating planar maps (graphs embedded in the sphere) with control over face degrees. In this paper, we extend the slice decompo…