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Article Dans Une Revue Discrete and Computational Geometry Année : 2019

Geometric realizations of the accordion complex of a dissection

Résumé

Consider $2n$ points on the unit circle and a reference dissection $D$ of the convex hull of the odd points. The accordion complex of $D$ is the simplicial complex of non-crossing subsets of the diagonals with even endpoints that cross a connected subset of diagonals of $D$. In particular, this complex is an associahedron when $D$ is a triangulation and a Stokes complex when $D$ is a quadrangulation. In this paper, we provide geometric realizations (by polytopes and fans) of the accordion complex of any reference dissection $D$, generalizing known constructions arising from cluster algebras.
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Dates et versions

hal-02343579 , version 1 (02-11-2019)

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Thibault Manneville, Vincent Pilaud. Geometric realizations of the accordion complex of a dissection. Discrete and Computational Geometry, 2019, 61 (3), pp.507-540. ⟨10.1007/s00454-018-0004-2⟩. ⟨hal-02343579⟩
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