Abstract
We show that the Simion type B associahedron is combinatorially equivalent to a pulling triangulation of the type A root polytope known as the Legendre polytope. Furthermore, we show that every pulling triangulation of the boundary of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the boundary of the Legendre polytope given by Cho. Finally, we extend Cho’s cyclic group action to the triangulation in such a way that it corresponds to rotating centrally symmetric triangulations of a regular (2 n+ 2) -gon.
| Original language | English |
|---|---|
| Pages (from-to) | 98-114 |
| Number of pages | 17 |
| Journal | Discrete and Computational Geometry |
| Volume | 60 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 1 2018 |
Bibliographical note
Publisher Copyright:© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Funding
Acknowledgements The authors thank the Princeton University Mathematics Department where this research was initiated. The first author was partially funded by the National Security Agency Grant H98230-13-1-028. This work was partially supported by grants from the Simons Foundation (# 429370 to Richard Ehrenborg, # 245153 and # 514648 to Gábor Hetyei, # 206001 and # 422467 to Margaret Readdy). The authors also thank the three anonymous referees for their comments.
| Funders | Funder number |
|---|---|
| Simons Foundation | 422467, 206001, 429370, 514648, 245153 |
| National Security Agency | H98230-13-1-028 |
Keywords
- Bott–Taubes polytope
- Compressed polytopes
- Cyclohedron
- Flag complex
- Stasheff polytope
- Type A root polytope
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics