Compatibility fans realizing graphical nested complexes
Abstrak
Graph associahedra are polytopes realizing the nested complex N(G) on connected subgraphs of a graph G.While all known explicit constructions produce polytopes with the same normal fan, the great variety of fan realizationsof classical associahedra and the analogy between finite type cluster complexes and nested complexes incitedus to transpose S. Fomin and A. Zelevinsky's construction of compatibility fans for generalized associahedra (2003)to graph associahedra. Using a compatibility degree, we construct one fan realization of N(G) for each of its facets.Specifying G to paths and cycles, we recover a construction by F. Santos for classical associahedra (2011) and extendF. Chapoton, S. Fomin and A. Zelevinsky's construction (2002) for type B and C generalized associahedra.
Topik & Kata Kunci
Penulis (2)
Thibault Manneville
Vincent Pilaud
Akses Cepat
- Tahun Terbit
- 2020
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.6400
- Akses
- Open Access ✓