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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
- Subject
- Mathematics; Combinatorics; Computational Mathematics and Numerical Analysis
- ISSN
- 0179-5376
- eISSN
- 1432-0444
- DOI
- 10.1007/s00454-018-0004-2
- Publisher site
- See Article on Publisher Site
Abstract
Consider 2n points on the unit circle and a reference dissection $${\mathrm {D}}_\circ $$ D ∘ of the convex hull of the odd points. The accordion complex of $${\mathrm {D}}_\circ $$ D ∘ is the simplicial complex of non-crossing subsets of the diagonals with even endpoints that cross a connected subset of diagonals of $${\mathrm {D}}_\circ $$ D ∘ . In particular, this complex is an associahedron when $${\mathrm {D}}_\circ $$ D ∘ is a triangulation and a Stokes complex when $${\mathrm {D}}_\circ $$ D ∘ is a quadrangulation. In this paper, we provide geometric realizations (by polytopes and fans) of the accordion complex of any reference dissection $${\mathrm {D}}_\circ $$ D ∘ , generalizing known constructions arising from cluster algebras.
Journal
Discrete & Computational Geometry – Springer Journals
Published: May 29, 2018