Each vertex in the above Hasse diagram has the ovals from the 3 adjacent faces. Faces whose ovals intersect do not touch.
In mathematics, an associahedron Kn is an (n – 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a string of n letters, and the edges correspond to single application of the associativity rule. Equivalently, the vertices of an associahedron correspond to the triangulations of a regular polygon with n + 1 sides and the edges correspond to edge flips in which a single diagonal is removed from a triangulation and replaced by a different diagonal. Associahedra are also called Stasheff polytopes after the work of Jim Stasheff, who rediscovered them in the early 1960s[1] after earlier work on them by Dov Tamari.[2]
- ^ Stasheff, James Dillon (1963), "Homotopy associativity of H-spaces. I, II", Transactions of the American Mathematical Society, 108: 293–312, doi:10.2307/1993609, MR 0158400. Revised from a 1961 Ph.D. thesis, Princeton University, MR2613327.
- ^ Tamari, Dov (1951), Monoïdes préordonnés et chaînes de Malcev, Thèse, Université de Paris, MR 0051833.