A type-B associahedron

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The (type-A) associahedron is a polytope related to polygon dissections which arises in several mathematical subjects. We propose a B-analogue of the associahedron. Our original motivation was to extend the analogies between type-A and type-B noncrossing partitions, by exhibiting a simplicial polytope whose h-vector is given by the rank-sizes of the type-B noncrossing partition lattice, just as the h-vector of the (simplicial type-A) associahedron is given by the Narayana numbers. The desired polytope QnB is constructed via stellar subdivisions of a simplex, similarly to Lee's construction of the associahedron. As in the case of the (type-A) associahedron, the faces of QnB can be described in terms of dissections of a convex polygon, and the f-vector can be computed from lattice path enumeration. Properties of the simple dual QnB* are also discussed and the construction of a space tessellated by QnB* is given. Additional analogies and relations with type A and further questions are also discussed. © 2003 Elsevier Science (USA). All rights reserved.




Simion, R. (2003). A type-B associahedron. Advances in Applied Mathematics. Academic Press Inc. https://doi.org/10.1016/S0196-8858(02)00522-5

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