Slit-slide-sew bijections for oriented planar maps
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. Mathematics Subject Classifications: 05A15, 05A19 Keywords: Bipolar orientations, Schnyder woods, combinatorial maps, enumeration, bijection, homomesy
Authors
- Jérémie Bettinelli (ORCID: https://orcid.org/0000-0002-0359-7493)
- Baptiste Louf (ORCID: https://orcid.org/0000-0002-7799-6948)
Institutions
- Centre National de la Recherche Scientifique (FR)
- École Polytechnique (FR)
- Laboratoire d'Informatique de l'École Polytechnique (FR)
- Institut Polytechnique de Paris (FR)
- Laboratoire d'Informatique Gaspard-Monge (FR)
- Université Gustave Eiffel (FR)
- Institut de Mathématiques de Bordeaux (FR)
Publication Details
- Journal
- Combinatorial Theory
- Published
- 2026-08-20
- DOI
- https://doi.org/10.5070/c6.68700
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Centre National de la Recherche Scientifique