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.
|Number of pages||17|
|Journal||Discrete and Computational Geometry|
|State||Published - Jul 1 2018|
Bibliographical noteFunding Information:
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.
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
- Bott–Taubes polytope
- Compressed polytopes
- 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