Séminaire Lotharingien de Combinatoire, 78B.32 (2017), 12 pp.

Richard Ehrenborg, Gábor Hetyei and Margaret Readdy

Realizing Simion's Type B Associahedron as a Pulling Triangulation of the Legendre Polytope

Abstract. We show that Simion's type B associahedron is combinatorially equivalent to a pulling triangulation of a type B root polytope called the Legendre polytope. Furthermore, we show that every pulling triangulation of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the Legendre polytope given by Cho. We extend Cho's cyclic group action to the triangulation in such a way that it corresponds to rotating centrally symmetric triangulations of a regular (2n+2)-gon.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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