Discrete Comput Geom https://doi.org/10.1007/s00454-018-0004-2 Geometric Realizations of the Accordion Complex of a Dissection 1 2 Thibault Manneville · Vincent Pilaud Received: 22 June 2017 / Revised: 29 March 2018 / Accepted: 21 April 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract 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. Keywords Permutahedra · Zonotopes · Associahedra · g-, c- and d-Vectors Mathematics Subject Classiﬁcation 52B11 · 52B12 · 13F60 Editor in Charge: Kenneth Clarkson Partially supported by the French ANR Grant SC3A (15 CE40 0004 01). Thibault Manneville firstname.lastname@example.org Vincent Pilaud email@example.com LIX, École Polytechnique, 91128 Palaiseau, France CNRS & LIX, École Polytechnique, 91128 Palaiseau,
Discrete & Computational Geometry – Springer Journals
Published: May 29, 2018
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