A type-B associahedron

39Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.

Abstract

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.

Cite

CITATION STYLE

APA

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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free