A tree bijection for Eulerian orientations on quartic maps

Marie Albenque; Enrica Duchi; Juliette Schabanel

A tree bijection for Eulerian orientations on quartic maps

Combinatorics 2026-07-24 v1

Authors: Marie Albenque , Enrica Duchi , Juliette Schabanel

Abstract

In this paper we construct a recursive bijection between $4$ -valent maps endowed with a Eulerian orientation -- also known as the ice model -- and a family of unary-binary trees. This answers a question of Bousquet-M\'elou and Elvey Price, who established that both these families have the same generating function in arXiv:2503.15046 .

Cite

@article{arxiv.2607.22208,
  title  = {A tree bijection for Eulerian orientations on quartic maps},
  author = {Marie Albenque and Enrica Duchi and Juliette Schabanel},
  journal= {arXiv preprint arXiv:2607.22208},
  year   = {2026}
}

Comments

22 pages, 15 figures