Slit-slide-sew bijections for oriented planar maps
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. Mathematics Subject Classifications: 05A15, 05A19 Keywords: Bipolar orientations, Schnyder woods, combinatorial maps, enumeration, bijection, homomesy
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Stochastic processes and statistical mechanics
Advanced Topology and Set Theory
Publication details
- Journal / source
- Combinatorial Theory
- Volume
- 6
- Issue
- 2
- Publication date
- 20 August 2026
- Language
- EN