Slit-slide-sew bijections for oriented planar maps
Combinatorics
2026-01-09 v2
Abstract
We construct growth bijections for bipolar oriented planar maps and for Schnyder woods. These give direct combinatorial proofs of several counting identities for these objects. Our method mainly uses two ingredients. First, a slit-slide-sew operation, which consists in slightly sliding a map along a well-chosen path. Second, the study of the orbits of natural rerooting operations on the considered classes of oriented maps.
Cite
@article{arxiv.2412.14120,
title = {Slit-slide-sew bijections for oriented planar maps},
author = {Jérémie Bettinelli and Éric Fusy and Baptiste Louf},
journal= {arXiv preprint arXiv:2412.14120},
year = {2026}
}