A type-B Tamari poset Original Research Article

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.