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arXiv · 1607.06061

Simion's type $B$ associahedron is a pulling triangulation of the Legendre polytope

Richard Ehrenborg·Gabor Hetyei·Margaret Readdy
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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. Finally, we present a bijection between the faces of the Simion's type $B$ associahedron and Delannoy paths.

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Richard Ehrenborg, Gabor Hetyei, Margaret Readdy. 2016-07-20. Simion's type $B$ associahedron is a pulling triangulation of the Legendre polytope. https://arxiv.org/abs/1607.06061

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