A realization of poset associahedra

Abstract

Given any connected poset $P$, we give a simple realization of Galashin's poset associahedron $\mathcal{A}(P)$ as a convex polytope in ${\mathbb{R}}^P.$ The realization is inspired by the description of $\mathcal{A}(P)$ as a compactification of the configuration space of order-preserving maps $P\to \mathbb{R}.$ In addition, we give an analogous realization for Galashin's affine poset cyclohedra.

13 pages, 7 figures. v2: minor revisions and exposition improvements

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