Regular Article: Convex Polytopes and Enumeration
Advances in Applied Mathematics
Non-crossing partitions for classical reflection groups
Discrete Mathematics
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
| Hi-index | 0.04 |
Let ΓnA denote the abstract simplicial complex whose elements are dissections of a convex (n + 2)-gon. Lee proved that ΓnA is the boundary complex of a convex polytope, now known as the associahedron. Simion constructed a type-B associahedron whose faces correspond to centrally symmetric dissections of a (2n + 2)-gon. In this paper, we define a partial order on the set of centrally symmetric triangulations whose Hasse diagram is the 1-skeleton of the simple B-associahedron and explore properties of this poset, including encodings, self-duality, and chain length. We also establish lattice failure and goodness.