Séminaire Lotharingien de Combinatoire, 86B.75 (2022), 12 pp.
Éric Fusy, Erkan Narmanli and Gilles Schaeffer
Enumeration of Corner Polyhedra and 3-Connected Schnyder Labelings
Abstract.
We show that corner polyhedra and 3-connected Schnyder labelings
can be set in exact correspondance with (weighted) bi-modal models of
quadrant walks via a bijection due to Kenyon, Miller, Sheffield and
Wilson.
Our approach leads to polynomial time enumeration algorithms, and to
the determination of their exact asymptotic growth constants, which
are rational. We use a heuristic argument to compute explicit but
conjectural polynomial corrections to these exponential behaviors,
that suggest that the corresponding generating series are not
D-finite.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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