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arXiv · 2412.14120

Slit-slide-sew bijections for oriented planar maps

Jérémie Bettinelli·Éric Fusy·Baptiste Louf
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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.

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Jérémie Bettinelli, Éric Fusy, Baptiste Louf. 2026-01-07. Slit-slide-sew bijections for oriented planar maps. https://arxiv.org/abs/2412.14120

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