Associahedron
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• Associahedra K, Y [claymath] (J.L. Loday) • Stasheff polytopes • Type A associahedra [arxiv] (Fomin, Reading) • Secondary polytope of the set of vertices of a polygon [maa review] (Gelfand, Kapranov, Zelevinsky) • Newton polytope of the discriminant polynomial of the (integer coordinate) vertices of a polygon. • Fiber polytope of the simplex over a polygon. [jstor] (Billera, Sturmfels) • Path graph associahedra [arxiv] (Carr, Devadoss) • Path graph cubeahedra [arxiv] (Devadoss, Heath, Vipismakul) • Zig-zag poset associahedra [arxiv] (Devadoss et.al.) • Quotientopes P , whose upper ideal of shards contains the basic shards and all upper shards. [Pilaud, Santos] • 2-associahedra W_n for the sequence(n). [arxiv](N. Bottman) • (1,n) biassociahedra KK(n,1), KK(1,n) [arxiv] (Saneblidze, Umble) • alt. notation B^n_1, B^1_n [arxiv] (Markl) • Constrainahedra C(1,n) = C(n,1), [ arxiv ] ( Bottman, Poliakova) or Constr(0,n) = Constr(n,0), [ arxiv ] ( Chapoton, Pilaud) |
• Dimensions: 0, 1, 2, 3, ... n • Number of Vertices in nth polytope: 1, 2, 5, 14, 42, ... Catalan numbers [ OEIS A000108] • Number of Facets: 0, 2, 5, 9, 14, ... Triangular numbers minus one [ OEIS A000096 ] • f-vectors: 1, 2, 1, 5, 5, 1, 14, 21, 9, 1, 42, 84, 56, 14, 1, ... [ OEIS A033282] • h-vectors: 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, 1, 15, 50, 50, 15, 1... [ OEIS A001263] |
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